﻿ Syllogisms - Syllogisms - Verbal Reasoning - How to Prepare for Verbal Ability and Reading Comprehension for the CAT ﻿

## How to Prepare for Verbal Ability and Reading Comprehension for the CAT (2014)

### Chapter 3. Syllogisms

SYLLOGISMS—THEORY

Syllogisms can be defined as a deductive scheme under which a formal argument is made. It consists of a major and a minor premise, leading up to a conclusion.

For example, let us look at the following example:

Major Premise: Every crime is deplorable;

Minor Premise: Eve teasing is a crime;

Conclusion: Eve teasing is deplorable.

Questions based on Syllogisms always first state the premises and then ask you to derive the conclusion on the basis of the relationship existing between the different elements of the premises.

The best method for solving syllogisms involves the use of Venn Diagrams. We will first look at the main types of premises and then look in detail at the process to be used to solve questions of syllogisms.

PREMISES—VARIOUS PATTERNS

A premise is defined as a proposition antecedently supposed or proved as a basis of argument or inference. In other words: something assumed or taken for granted.

Type 1: All A’s are B’s (Or No A is not B):

There are two possible Venn diagrams for this situation. These are:

The following reactions to the premise All A’s are B’s are valid:

(a)Some B’s are A’s. This is a definite conclusion.

This is true in both Figures A and B.

(b)Some B’s are not A’s. This is a probable conclusion and will occur only if the conclusion All B’s are A’s is not true.

Hence, it can be stated that if All A’s are B’s, then either All B’s are A’s (No B is Not A) or Some B’s are not A’s. As can be seen in the figures above, either Some B’s are not A’s (Figure A) or All B’s are A’s (as seen in Figure B).

Type 2: Some A’s are B’s

This premise is represented by the following figure:

The valid reaction to this premise is:

Some B’s are A’s

This is a definite conclusion (as can be seen clearly in figure A above.)

Although the above figure also supports the conclusion —some B’s are not A’s, this cannot be taken as a definite conclusion. This is because, when we say that Some A’s are B’s, it does not mean that there have to be some B’s that are not A’s.

Type 3: No A is B

This premise is represented by the following figure:

The conclusion No B is A is a valid conclusion.

Type 4: Some A’s are not B (Or All A is not B)

There could be three possible Venn Diagrams in this case, as shown below:

STANDARD PROCESS FOR SOLVING SYLLOGISM QUESTIONS

The most logical process of solving Syllogism questions is through Venn diagrams. The following examples will make the process clear:

Solved Examples

1.(A) All tigers lays eggs. (B) All cats lay eggs.

(C) Some cats can fly. (D) All tigers cannot fly.

(E) All tigers are cats. (F) All tigers cannot swim.

(a) BEA         (b) ABE

(c) DEC         (d) ECB

In the above question, it can be clearly seen that the sequence BEA is the most appropriate since if all cats lay eggs is true and it is also true that all tigers are cats, then it will also be true that all tigers lay eggs.

2.(A) Some curtains are cloth. (B) All cloth is wood.

(C) All that is wood is cloth. (D) All cloth are curtains.

(E) All curtains are wood. F. Some curtains are wood.

(a) BED         (b) BDF

(c) FAB         (d) FBA

BDF is the most logical sequence here since if we take B and D as the premises, then the curtains which are cloth, will also be wood.

The Venn diagram for BD will look like this—

Hence, F is the correct conclusion.

3.(A) All balls are talls. (B) Some talls are dolls.

(C) Some dolls are balls. (D) Some talls are not balls.

(E) All talls are dolls. (F) No talls are dolls.

(a) EAC         (b) BCD

(c) ABC         (d) EDC

EA will give the following figure which will give C as the conclusion. Hence, the answer is (a).

4.(A) Some stone is bone. (B) All slipper is bone.

(C) All bone is stone. (D) No stone is slipper.

(E) No bone is stone. (F) Some bone is slipper.

(a) BCA         (b) AFE

(c) DEC         (d) CEA

(CAT 1996)

(a) is the obvious answer here, since if all bone is stone (C), then obviously, some stone is bone (A).

5.(A) No rice is a pest. (B) All pest is lice.

(C) Some rice is lice. (D) All rice is pest.

(E) All rice is lice. (F) No rice is lice.

(a) BEF         (b) FCB

(c) ABF         (d) BDE

BDE will give the following Venn Diagram which makes E the correct conclusion for the premises BD.

6.For this question, you have to base your conclusion on the three premises (viz: a, b and c). Identify the correct answer from amongst the options given to you:

 Statements a. Some cakes are bikes b. Some bikes are hills c. All laptops are bikes Conclusions I. All laptops are hills II. Some laptops are cakes III. Some cakes are hills IV. Some laptops are not cakes

(1)Only I follows

(2)Only either II or IV follows

(3)Only I or III follow

(4)Only I and IV follows

(5)None of these

For the question above, the following Venn Diagram can be drawn:

It is clear from the figure that the conclusion ‘All Laptops are Hills’ does not hold.

Similarly, some Cakes are hills is also not necessarily true. If we take a look at II & IV, we can conclude that one of them has to be true. Hence, the answer is (2).

7.(A)No hyenas laugh. Some who laugh are lions. Some lions are not hyenas.

(B)All ghosts are red. Some ghosts do not dance. Some dancers are not red.

(C)Australians indulge in swearing. Those who swear are fined. Some who are fined are not Australians.

(D)Some Europeans are Spanish. All Europeans are British. Some British are Spanish.

(a) A and B         (b) C only

(c) A and D         (d) D only

The following Venn Diagram can make for the sequence A:

Obviously, the lions who laugh are not hyenas. Hence, the conclusion is justified.

The following Venn Diagram will be made for the sequence D:

It is obvious that whatever circle we draw for Spanish (apart from the one shown) it will have to intersect the circle for Europeans. This in effect, means that, it has also to intersect with the British circle. Hence, the conclusion that ‘Some British are Spanish’ is justified.

8.(A)All Pakistanis are brave. All baskets are Pakistanis: All brave are baskets.

(B)No golfers are Asian. All golfers are athletic. Some Asians are pros.

(C)All burgers are chips. Some refreshments are burgers. Some refreshments are chips.

(D)Some bowlers are fast. All bowlers are spinners. Some spinners are fast.

(a) C and D         (b) Band C

(c) A only           (d) C only

The following Venn Diagram can be made for the sequence C:

The conclusion for C is justified in exactly the same way as the one for the sequence D of Solved Example 7.

The following Venn Diagram can be made for sequence D:

As is clear from the diagram above, the conclusion is justified on the basis of the same logic as for the last two diagrams.

Practice Exercises

Type 1

Directions for Questions 1 to 10: In each of the questions below are given two statements followed by two conclusions numbered I and II. You have to take the two given statements as true even if they seem to be at variance with commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follow(s) from the given statements, disregarding commonly known facts.

 Give answers (a) if only conclusion I follows. (b) if only conclusion II follows. (c) if either I or II follows. (d) if neither I nor II follows (e) if both follow 1. Statements: (A) All cats are dogs. (B) All dogs are brown. Conclusions: I. All cats are brown. II. All brown are dogs. 2. Statements: (A) All computers are pentiums. (B) Some pentiums are machines. Conclusions: I. Some computers are machines. II. Some machines are computers. 3. Statements: (A) Some apples are fruit. (B) Some fruits are sour. Conclusions: I. Some apples are sour. II. Some sours are fruit. 4. Statements: (A) Some rods are sticks. (B) Some scales are rods. Conclusions: I. Some sticks are rods. II. Some scales are sticks. 5. Statements: (A) Architects marry only fair girls. (B) Bimla is very fair. Conclusions: I. Bimla was married to an Architect. II. Bimla was not married to an Architect. 6. Statements: (A) Sehwag is a good batsman. (B) Batsmen are physically powerful. Conclusions: I. All physically powerful are Batsmen. II. Sehwag is physically powerful. 7. Statements: (A) Some cats are white. (B) Milk is white. Conclusions: I. Some cat is milk. II. Some white is milk. 8. Statements: (A) All pens are long. (B) All pencils are long. Conclusions: I. All pens are pencils. II. Some pens are pencils. 9. Statements: (A) All resorts have scenery. (B) Mahabaleshwar is a resort. Conclusions: I. Mahabaleshwar has scenery. II. Places other than resorts don’t have scenery. 10. Statements: (A) All teenagers go to cinema. (B) Raveesh doesn’t go to cinema. Conclusions: I. Raveesh is not a teenager. II. Going to cinema is not essential to be a teenager.

Type 2

Directions for Questions 11 to 40: In each of the questions below are given three statements followed by four conclusions numbered I, II, III and IV. You have to take the three given statements to be true even if they seem to be at variance with commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follow(s) from the given statements disregarding commonly known facts.

Type 3

Directions for Questions 51 to 70: Each question contains six statements, followed by four options of combinations of any three of the given sentences. Choose the option in which the combinations are logically related.

Type 4

Directions for Questions 71 to 75: Each question contains four arguments of three sentences each. Choose the set in which the third statement is a logical conclusion of the first two.

 71. I. Some Xs are Ps. Some Ps are Ys. Some Xs are Ys. II. All Chandis are beautiful. Some beautiful are crazy. Some Chandis are crazy. III. No belief is strong. Only strong have muscles. No belief has muscles. IV. All orangutans are men. Some men are strong. Some orangutans are strong. (a) I and IV (b) III only (c) IV only (d) None of these 72. I. Some bikes are mopeds. All mopeds are scooters. Some bikes are scooters. II. All children are hairs. No hairs are red. No children are red. III. No pencil is pen. Some pens are markers. Some pencils are markers. IV. Every man has a wife. All wives are devoted. No devoted has a husband. (a) I, II and III (b) I and II (c) III and II (d) I, II and III and IV 73. I. No moon is not red. All stars are moon. All stars are red. II. All doors are open. No open is outdoors. All doors are not outdoors. III. No Japanese can fire. All Chinese are books. Japanese and Chinese can fight. IV. No A is B. No B is C. No A is C. (a) I only (b) II only (c) I and II only (d) IV only 74. I. All envelopes are rectangles. All rectangles are rectangular. All envelopes are rectangular. II. Some thin are smart. Some smart things are tiny. Some thin are tiny. III. Learneds are well read. Well read know. Learneds know. IV. Dieting is good for health. Health foods are rare. Dieting is rare. (a) IV only (b) III only (c) Both I and III (d) All of these 75. I. Shahrukh is an actor. Some actors are pretty. Shahrukh is pretty. II. Some executives are soldiers. All soldiers are patriotic. Some executives are patriotic. III. All cricketers are patriotic. Some executives are soldiers. Some executives are patriotic. IV. All actors are pretty. Shahrukh is not an actor. Shahrukh is not pretty. (a) IV only (b) II only (c) I only (d) II and III