BASICS ON SYLLOGISMHello Readers, We are providing some basic of Syllogism that will clarify your doubts to some extent. Also, practice the questions given below!!! 1 | Page Directions (1 - 11): In each question below are given two or three statements followed by two conclusions numbered I and II. You have to take the two given statements to be true even if they seem to be at variance with commonly known facts. Read both the statements and then decide which of the given conclusions logically follows from the given statements, disregarding commonly known facts. Give answers: Give answer (1) if only conclusion I is true. Give answer (2) if only conclusion II is true. Give answer (3) if either conclusion I or II is true. Give answer (4) if neither conclusion I nor II is true. Give answer (5) if both conclusions I and II is true 1. Statements: Some apples are mangoes. Some mangoes are oranges. No orange is apple. Conclusions: I. some mangoes that are oranges are apples II. some apples that are mangoes are oranges 2. Statements: Some birds are animals. All animals are black. No black is white. Some whites are birds. Conclusions: I. Some birds which are black are not white. II. All animals which are black are necessarily bird. 3. Statements: All scooters are buses. All bikes are buses 50% buses are trains Conclusions: I. All buses are either bikes or scooters. II. Some scooters being train is a possibility 4. Statements: All apples which are red is tasty. Most reds are apples. 2 | Page Most apples are balls Conclusions: I. Some reds are tasty. II. Some apples are neither red nor ball. 5. Statements: All cups are plates. Some plates are bowls. Conclusions: I. Some bowls if they are cups, are also plates. II. All bowls which are not plates are also not cups. 6. Statements: Some roses which are plants are flowers. All plants are lotus. Conclusions: I. Some lotus are not flowers. II. Some lotus which are roses are flowers. III. Some roses are lotus. 7. Statements: All matches are cups. Some fields are not viewers. All viewers are fans. Some matches are not fans. Conclusions: I. Some cup which are fans are not viewers. II. Some matches which are not viewers are cups. III. Some fields which are fans are not matches. 8. Statements: Some pens are books. Some books are pencils. Some pencils are rubbers. All books are slates. Conclusions: I. All pencils are books. II. All pens are pencils. III. Some slates are pens. IV. All slates are books 3 | Page No college is a principal. Conclusions: I.9. Some flowers which are roses are not sunflowers. III. II. All colleges are schools. 10. Some cats are not Kangaroos. Some animals who are not elephants are not kangaroos. II. II. Some sunflowers which are leaves are not plants. Conclusions: I. ANSWERS 1. No Kangaroo is animals. Some roses which are plants are not flowers. (1) 4 | Page . Some principals are colleges. All elephants are cats. All schools are principals. Statements: Some schools which are not students are colleges. 11.Statements: Some animals are not cats. Statements: All roses which are leaves are flowers. Conclusions: I. (4) 2. No student is a principal. (1) 5.3. (5) 6. (2) 4. (2) 5 | Page . (3) 7. (3) 6 | Page .8. (3) 9. (1) 11. (3) 10. Piscine Molitor (Pi) again provided us one of his magnificent post on "Syllogism at its Best". No A are B 3. Some B are A 6. and whoosh. let’s start from the basic statements Statement 1: All A are B Now.SYLLOGISM AT ITS BEST Hello Readers. here we are providing you the same. seeing if they’re fitting in their circles or not. crossed the wrong ones. wrong answer! Now. All B are A 5. Some A are not B 4. they first made all the conclusions and then they headed on the conclusion. Some A are B 2. Don't forget to thank him!!! I’m sure most people would have tried to do these questions. Then they ticked the right conclusions. I’d like make you understand this trick of picking up the right conclusions!! The trick is “One statement has many conclusions!!” Now. with the wrong conclusions. So. let’s try all these conclusions if they fit in this statement 1. in this post. No B are A 7 | Page . What they did are. So. let’s try all these conclusions if they fit in this statement 1. Some B are not A will not follow. can follow. some B are A 6th? Bullshit conclusion. All A are B and All B are A 5th? Of course. In that case. Some A are not B 8 | Page .7. How can no B are A 7th? Well. look at 4th conclusion. i. Its possible that All B are A if A also encircles B. that means Some A are Definitely B Is conclusion 2 following? Of course not! What about 3rd? Yes yes. Not following 4th? Well. if A encircles B. there’s a possibility that this 7th conclusion will follow. Some B are not A Is conclusion 1 following? Yes! Of course! All A are B.e. All A are B 2. Understood? Statement 2: Some A are B Now. No A are B 3. but yes. In all cases. but it’s possible. 3rd? It won’t follow in all the cases. Some B are not A Is conclusion 1 following? Could follow. it also could be possible. Some B are A 6. All Bare A 5. 5th? Yes. Statement 3: No A are B Now. 6th? Impossible. let’s try all these conclusions if they fit in this statement 9 | Page .Nahinahinahi! 7th? It could be possible. Won’t follow in all the cases. Follow.4. it’s possible. No Bare A 7. 2nd? Impossible. 4th? Again. not following! 5th? What the hell.1. then Some A are also Not B. follows! 7th? 10 | P a g e . Yes.. 3rd? No A are B. Some B are A 6. Some A are not B 4. Some B are not A Conclusion 1 following? Of course not! 2nd? Haha.. Not following! 6th? Now this is class. No Bare A 7. Some A are B 3. Yes. following! 4th? Clearly. All Bare A 5. All A are B 2. All A are B 2. Some B are A 6.Of course will follow! No A are B only means. Some A are B 3. Could be possible! 11 | P a g e . could be possible! 4th? Yes. Some B are not A Is conclusion 1 following? Of course not! 2nd? It could be possible! Not in all cases. yes. but it could be possible 3rd? Again. AllB are A 5. which also means. No A are B 4. No Bare A 7. No B are A. Some B are not A Statement 4: Some A are not B Now. let’s try all these conclusions if they fit in this statement 1. Some pencil boxes are mugs. All mugs are lunchboxes. II. possible! Now. Conclusions: I. but could be possible! 6th? Again. Some buckets are not drums. Question 1: Statements: All buckets are mugs. let’s solve some basic questions based on all the things that we’ve just learned.5th? Not in all cases. 12 | P a g e . All lunchboxes are buckets. it also could be possible! 7th? Again. All lunch boxes are pencil boxes. Some tables are benches. Some desks are benches. Some benches are desks. IV. Some lunchboxes are mugs.III. II. 1? Not follows 2? Not follows 3? Not follows 4? Not follows Question 2: Statements: Some chairs are tables. Conclusions: I. Some drums are not mugs. III. Some woods are not benches. Some desks are tables. All benches are tables. IV. 1? Yes 2? Yes 3? Not follows 4? Yes Question 3: 13 | P a g e . Some woods are not desks. 1? Not Follows 2? Yes. IV.Statements: No bank is a market. Some markets are not rooms. Some fives are threes. III. Some twos are fives. II. Some rooms are restaurants. All five are fours. II. Some threes are fours. Conclusions: I. Some twos are fours 14 | P a g e . IV. III. Some banks are rooms. Some restaurants are markets. Conclusions: I. Some offices which are Market cannot be Banks 3? Not follows 4? Not follows Question 4: Statements: All ones are twos. Some markets are offices. All three are ones. Some ones are fives. Some offices are not banks. All restaurants are offices. so many diagrams are possible!! In possibility questions. Some trees are houses C.PART . then the conclusion is false. As simple as that! Keeping this and also the previous Syllogism Post in mind. Follows SYLLOGISM AT ITS BEST . 15 | P a g e . Yet another marvellous post by Piscine Moliter (Pi) on "Possibility cases in Syllogism and solving them using Venn Diagrams". So. let’s solve some possibility questions. All flowers are trees B. If not.II . then the conclusion holds true. If there exists at least one such case. We couldn't thank you enough Pi!! Recall the previous article in which we had studied these basic things: A statement has many conclusions (cases) And thus. Abbreviations that I used: Basic Diagram = BD Modified Diagram = MD Question 1: Statements: A.1? Not follows 2? Not follows 3? Not follows 4? Yes. All houses are wheels Let’s first make a BD according to these statements. the examiner asks if there exists any such case (diagram) where this conclusion is valid. you job is to find out this case. Conclusions: 1. All wheels are flower is a possibility Now. Conclusion 2 also clearly follows. Conclusion 3 follows. we can clearly see that all the statements are still valid. what about Conclusion 3? Let’s make a MD and see if it follows or not! In the MD. 1? Follows 2? Follows 3? Follows Understood? Let’s now solve another question! Question 2: 16 | P a g e . Some trees are flowers 3. and Conclusion 3 also is following. So. At least some wheels are trees 2. But. see the BD. Conclusion 1 clearly follows. At least some drawers are desks 2. Some pens are drawers First. Some desks are chairs B. make a BD according to these statements.Statements: A. No drawer is a chair Now. Conclusion 3 will not follow! 1? Doesn’t follows 2? Follows 17 | P a g e . Some chairs are pens C. There is a possibility all drawers are chairs 3. Conclusion 2 follows in it. then how could No drawer is a chair follow? So. what about Conclusion 2? Let’s make a MD See the MD. But. Conclusions: 1. And if there is a possibility that All drawers are chairs. see the BD Conclusion 1 clearly doesn’t follow. Conclusion 2 clearly follows! 18 | P a g e . 3? Doesn’t follows Understood? Let’s solve another one! Question 3: Statements: A. Conclusion 1 clearly follows. Some politicians are not leader 2. So. Some politicians. Some politicians are honest C. make a BD according to these statements. cannot beleaders. No leader is honest First. which are honest (Red Portion). Conclusions: 1. But. see the BD. See the MD. All politicians are corrupt B. Some leaders are not corrupt Now. All honest being corrupt is a possibility 3. what about Conclusion 2? Let’s make a MD. 1? Follows 2? Follows 3? Doesn’t follows Understood? Question 4: Statements: A. Some honest are people 19 | P a g e . See the last diagram. Conclusions: 1. Conclusion 3 doesn’t follow.What about conclusion 3? Let’s make another MD. All leaders are corrupt could be a possibility! So. No intelligent is smart First. All intelligent are honest C. All people being honest is a possibility 3. Some honest are not smart 2. make a BD according to these statements. Some people are intelligent B. See the MD. cannot be smart. Conclusion 1 follows. Conclusion 2 clearly follows. Conclusion 3 also follows. see the BD. But.Now. So. what about Conclusion 2? Let’s make a MD. Some honest. 1? Follows 2? Follows 3? Follows Understood? Question 5: Statements: 20 | P a g e . which are intelligent (Red Portion). Hence. See the MD. All poets being actor is a possibility 4. so. Also. Some actors are not dancers 3. some actors. Conclusions: 1. cannot be dancers. Conclusion 1 clearly follows. But. Some writers are poets B. Many singers are actors D. no poet is a dancer. what about Conclusion 3? Let’s make a MD. Conclusion 2 also follows. Also. No poet is a dancer See the BD. since no singer is a dancer. make a BD according to these statements. Some writers are singers 2. So.A. Conclusion 3 clearly follows. which are singers (Red Portion). Conclusion 4 is also following! 1? Follows 2? Follows 3? Follows 4? Follows 21 | P a g e . No singer is a dancer First. All poets are singers C. Proposition/Premise = Quantifier+ Subject+ Copula+ Predicate. . Subject: The subject is that about which something is said. No. Some. Quantifier: All. Example All/Some etc. Atleast. But the problem is that it is tedious. Copula: it denotes the relation between the subject and the predicate. Atmost etc. All/No: Universal Quantifiers(as it refers to every object in a certain set) Some/Atleast/Atmost: Particular Quantifiers(as it refers to atleast one existing object in a certain set).Subject Are . Prakash Guru again provided us one of his magnificent post on "Syllogism (Logical Deduction)". 3. One way to solve syllogism is the Venn-Diagram method.Quantifier Men . Hope the following note helps one and all!! “Syllogism” is a deductive argument in which conclusion has to be drawn from two propositions referred to as premises. Trivia: It was introduced by Aristotle.Copula 22 | P a g e . Hope everybody agrees with it. here we are providing you the same. lengthy and complicated too. Predicate: The predicate is that part which is being affirmed /denied. 2. Don't forget to thank him!!! I faced lots of problem in solving these problems until I went through the logic behind it. 4.Understood? Syllogism (Logical Deduction) Hello Readers. 1. So. P= Predicate 23 | P a g e Examples Statement: All men are fools Valid Conclusion: some fools are men Statement: No men are fools Valid Conclusion: No fools are men Statement: Some men are fools Valid Conclusion: Some fools are men .Predicate Classification of Propositions: Universal affirmative proposition or Type. some men are foolish. All Snakes are reptiles. P= Predicate Both S and P Neither S nor P Only P Table 2: Rule of Conversion: (Memorize this) Statement form All S is P Valid Conversion/ Conclusion Some P is S No S is P No P is S Some S is P Some P is S Some S is not P No valid Statement: Some men are not fools Conversion Valid Conclusion:---S: Subject. Particular Negative or Type-O : ex.A: ex. No boy is Intelligent Particular Affirmative or Type-I: ex. Animals . Universal Negative Proposition or Type-E: ex. some animals are not wild Table 1: Summarizing the above propositions (Memorize this) Statement form Quantity Quality Distribution All S is P Universal S only No S is P Universal Affirmativ e Negative Some S is P Particula Affirmativ r e Some S is not Particula Negative P r S: Subject. All mens are girls 2. The conclusion should not contain the middle term. Dogs: is common to both the premises and hence termed as the middle term Note: Of the two premises.Syllogism is concerned with 3 terms: Major Term: It is the predicate of the conclusion and is denoted by “P”. b. Animals: is the predicate of the conclusion and hence the major term. All Tigers are dogs. if not read once again!! Rules for deriving the conclusion from 2 premises: (MAJOR PART-READ CAREFULLY AND MEMORIZE ALL THE CONDITIONS) a.e. Conclusion: All tigers are animals Here. SO GUESS YOURSELF IN THE ABOVE PREMISES WHICH IS THE MAJOR AND WHICH IS THE MINOR ?? P. as the middle term i. Explanation: In the above example neither of the conclusion is valid. girls is present in both the conclusions. No term can be distributed in the conclusion unless it is distributed in the premises. Minor term: It is the subject of the conclusion and is denoted by “S”. Conclusion: Some girls are men . 24 | P a g e . all girls are men.S: If you find the answer you have studied this well. All dogs are animals 2. Some girls are students. the major premise is that in which the middle term is the subject and the minor premise is that in which the middle term is the predicate. Tigers: is the subject of the Conclusion and hence the minor term. Example Premises 1. An Example to make you clear about the terms: Premises: 1. Middle term: It is the term common to both the premises and is denoted by “M”. e.: 1. d. All goats are cows. Some flowers are petals (No conclusion can arise from the above two premises other than the conversions). some dogs are cows. Ex.: Premises: 1. E-type. Statement type A Distribution Condition E "M" must be Subject/Predicate O "M" must be predicate I Cannot be distributed/Not distributed "M" must be Subject Ex. Some watches are black In the above premises the middle term is “watches”. in conclusion 1 the term “Cow “is distributed but it is not distributed in the premise i. Explanation . Some dogs are goats 2. Some balloons are flowers 2. c. If major premise is particular and minor is negative 25 | P a g e .e premise-2 since it is a A-type proposition and the term “Cow” to be distributed must be the “subject” (Refer table-1) of the proposition. Ex. otherwise no conclusion follows. The middle term (M) should be distributed at least once in the premises. other than their conversions). All fans are watches 2. If both premises are negative i. since it is not distributed in both premises(refer above table for distribution conditions) no conclusion can be drawn except the conversions of the premises. No conclusion follows: If both premises are particular i. No ship is a boat 2.Here. Conclusions: All cows are dogs. 1.e I type.Example Premises: 1. No boat is a vessel (No conclusion can be deducted from the above statements. (Here the conclusion must be “All womens are sisters”) The above conditions when applied on syllogism problems.All fans are chairs 2. 1. If both premises are universal affirmative. What is a complementary pair? Sometimes there is an option like “either 1 or 2 follows”. The pairs that make a complementary pair are I-O type. Try it yourself.Ex. g. 1. the conclusion cannot be Universal. thus premise 2 is the minor and it is negative. makes the problems easy. 1. 1. Ex. Some dogs are bulls 2. the conclusion must be negative.e “some boys are dacoits”. the conclusion should be universal affirmative. No tigers are dogs (Here “dogs” is the middle term and it is present in the subject part of the first premise which makes it the major premise. Ex. rather the conclusion will be “Some chairs are not tables” i. All grasses are trees 2. ( As the middle term “fans” is distributed twice in the above premises. If one premise is particular. No tables are fans. 1. Some boys are thieves 2. All mothers are sisters. the conclusion must be particular.) e. If the middle term is distributed twice. A-O type or I-E type given that the subject and predicate remains same in both the statements.e particular negative-O type) f.e “No chairs are tables”. Ex. All thieves are dacoits (Here the conclusion must be particular i. All womens are mothers 2. This is because of a complementary pair in the conclusions. No tree is a shrub Conclusion: Here the conclusion that will arise from the above premises is “No grass is a shrub” as the middle term tree is only distributed in the second premise and one premise is negative). since the middle) h. To explain this lets consider the following examples: 26 | P a g e . If one premise is negative. the conclusion cannot be universal i. Ex. thus as per the condition no conclusion can arise from the premises other than their conversions. R. In pair-I the first statement is of type A and the second is of type O and thus an A-O type pair makes a complementary pair. Pair I: i. as from two conclusions or from one conclusion and another premise another conclusion can be obtained. Statements: All buckets are mugs.) All gardens are bulbs ii. 27 | P a g e .S Aggarwal and practice problems Solve Quiz given by BA on syllogism. Pair IV: i. because they are really good. Similarly pair II and Pair III makes I-O and I-E type of pair respectively thus it makes a complementary pair. Pair V is and A-O type pair but still do not make a complementary pair. Remember always about the conversions. because maximum times the conclusions are in the form of conversions only. Pair IV is an A-E type of pair and thus it do not make a complementary pair.) Some gardens are not bulbs Pair II: i.) No gardens are bulbs Pair V: i. Once you do a lot of problems I am sure you needn’t even write the problems you will just look at the premises/proposition and derive all the possible conclusions. since the subject and predicate are jot same in both the statements.) Some gardens are bulbs ii.) All gardens are bulbs ii. Refer books like BSC and Dr.) No gardens are bulbs. All lunch boxes are pencil boxes.) Some gardens are not bulbs Pair III : i.) Some bulbs are not gardens. II and III make a complementary pair each while Pairs IV and V don’t. Some Important Tips: Practice as many problems as possible and you will automatically remember the logics that I have shared. Try all possibilities.) Some gardens are bulbs ii. Now let us decipher the quiz put by BA on 17/9/2014 1. Explanation: Pairs I.) All gardens are bulbs ii. 2. Some desks are tables. (1) Only III follows (2) Only I and III follow (3) Only I. IV. III. and a careful analysis shows nothing such. IV. now check the conclusions for a complementary pair or a conversion of the any statements. III. II and IV follow (4) Only II and IV follow (5) None of these Solution with explanation: Here we can only compare. All lunchboxes are buckets. premise 2 and premise 3. Statements: Some chairs are tables. Some lunchboxes are mugs. and premise 3 is I-type. All benches are tables. so middle term cannot be distributed. premise 2 and premise 3 have pencil boxes as the middle term. In premise 1 and premise 4 the middle term is buckets and is also distributed in one premise that is premise 1 but the predicate if different. Some buckets are not drums. Some drums are not mugs. Conclusions: I. II. (1) Only III follows (2) Only I and III follow (3) Only II and III follow (4) None of these (5) Only II follows Solution with explanation: Here. Some benches are desks. Conclusions: I. Some tables are benches. So. but it is not distributed in any of the premises since premise 2 is A-type. Thus the answer is 4-None follows. Some desks are benches. In the said premises the middle term is benches and it is distributed in premise 3 and one premise is particular so the conclusion shall be particular and without the middle term i. thus no conclusion follows. so the middle term must be the subject but it is in the predicate.Some pencil boxes are mugs. thus no conclusion can arise from the statements. Some woods are not benches. Some woods are not desks. II. All mugs are lunchboxes.e “Some desks are 28 | P a g e . Some threes are fours. Some twos are fours. middle term being “banks” so conclusion shall be particular negative without the middle term i. (1) Only I and II follow (2) Only II follows (3) Only I. Some ones are fives. IV. Statements: All ones are twos. II and III follow (4) Only I and III follow (5) None of these Solution with explanations: See premise 1 is negative and premise 2 is particular and the middle term “markets“ is distributed in premise 1 thus the conclusion shall be particular negative without the middle term i. Some fives are threes. Some markets are not rooms. (1) Only I and IV follow (2) Only IV follows (3) Only II and IV follow (4) None of these (5) Only I follows 29 | P a g e . now premise 1 and premise 4 have the same conditions. Statements: No bank is a market. So only conclusion II follows. Some banks are rooms. All three are ones. All fives are fours. Conclusions: I. Thus Only I. 3. Conclusions: I. All restaurants are offices.e “some offices are not banks”. III.option 2. Some markets are offices.e “some rooms are not market” but conclusion 1 is “some markets are not rooms” which is not similar as there is no valid conversion for a particular negative statement.tables” which matches the conclusion IV and there is no complementary and conclusion I and II are conversions of premise 2 and premise 3. II. II. Some restaurants are markets. Some offices are not banks. Some rooms are restaurants. III. Some twos are fives.II and IV follows-that is option 3. IV. 4. (1) Only I and III follow (2) Only I and II follow (3) Only II follows (4) Only II and IV follow (5) None of these Solution with Explanation: Comparing Premise 1 and 2 we get the conclusion as “Some icecreams are biscuits” with is conclusion II.e “All one are twos” we get “some fours are twos”. Statements: Some ice-creams are cakes. thus only Conclusion IV follows-option 2 is your answer. II. IV.option 4 is your answer. III. Some ice-creams are biscuits.. Some biscuits are parles. 30 | P a g e . the conversion being “some twos are fours” which is conclusion IV. All cakes are biscuits. All ice-creams are biscuits. Some toffees are biscuits. Conclusions: I.Solution with explanation: From premise 2 and 3 we get “some fours are ones” now making this as a premise and comparing with premise 1 i. Some parles are toffees. 5. the conversion of this conversion is “Some cakes are biscuits” which is conclusion IV thus only II and IV follows. Now statement 1’s conversion is “Some biscuits are cakes”. Some cakes are biscuits.
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