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Worked Examples: Type I

In each question below are given two statements I and II, followed by two conclusions namely, A and B. You have to take the two given statements to be true even if they seem to be at variance from the commonly known facts and then decide which of the given conclusions logically follow from the two given statements, disregarding the commonly known facts.
  1. If only conclusion ‘A’ follows.
  2. If only conclusion ‘B’ follows.
  3. If either ‘A’ or ‘B’ follows.
  4. If neither ‘A’ nor ‘B’ follows.
  5. If both ‘A’ and ‘B’ follow.

Example-1

St. I—All cars are chairs.

 

St. II—Some girls are chairs.

 

Con A—Some cars are girls.

 

Con B—Some girls are cars.

Solution

The first premise is an ‘A’ type proposition. So the middle term ‘chairs’ forming the predicate is not distributed. The second premise is an ‘I’ type proposition. So, the middle term forming the predicate is not distributed. Since the middle term is not distributed at least once in the premises, no conclusion follows (rule 2).

 

Answer: (4)
 

This problem can also be analysed with the help of logical Venn diagrams.

 

The given statements can be represented by using Venn diagram as under:

 

Description: 110681.png

 

From the above diagram, we can infer that none of the given conclusions follow.
 

 

Example-2

St. I—All cakes are ice creams.

 

St. II—All ice creams are pizzas.

 

Con A—All cakes are pizzas.

 

Con B—All pizzas are ice creams.

Solution

Since both the statements are affirmative, the conclusions must be affirmative (rule 8). Further, in conclusion A the term ‘cakes’ is distributed and in statement I also this term is distributed. So, conclusion A follows.

 

Conclusion B is an immediate inference drawn from statement II. The term ‘pizzas’ is distributed in conclusion B and it is not distributed in any of the premises. So, conclusion B does not follow.

 

Answer: (1)
 

Analysis with Venn diagram.

 

Description: 110692.png

 

From the above diagram, we notice that all cakes are pizzas, but all pizzas are not ice creams. Hence, only conclusion A follows.
 

 

Example-3

St. I—All men are prisoners.

 

St. II—No prisoners are urban.

 

Con A—All prisoners are urban.

 

Con B—No men are urban.

Solution

Since the second premise is negative, the conclusion must be negative (rule 7). Further, the term ‘urban’ is distributed both in statement II and in conclusion B. So, only conclusion ‘B’ follows.

 

Answer: (2)
 

Analysis with Venn diagram.

 

Description: 110701.png

 

From the above diagram, it is clear that no men are urban. Hence, only conclusion B follows.
 

 

Example-4

St. I—All men are married.

 

St. II—Some men are educated.

 

Con A—Some married are educated.

 

Con B—Some educated are married.

Solution

Since one premise is particular, the conclusion must be particular (rule 6). So both the conclusions ‘A’ and ‘B’ follow.

 

Answer: (5)
 

Analysis with Venn diagram.

 

Description: 110710.png

 

From the diagram, it is clear that some men are educated and some educated are married. Hence, both the conclusions follow.
 

 

Example-5

St. I—All puppets are flowers.

 

St. II—All flowers are toys.

 

Con A—Some toys are puppets.

 

Con B—All toys are puppets.

Solution

In conclusion B, the term ‘toys’ is distributed. But, the term ‘toys’ is not distributed in any of the premises. So, conclusion B does not follow (rule 1).

 

Since both the premises are affirmative, the conclusion should be affirmative (rule 8). This condition is satisfied in conclusion A. Moreover, no term is distributed in the conclusion. So, conclusion A follows.

 

Answer: (1)
 

Analysis with Venn diagram.

 

Description: 110718.png

 

From the diagram, it is clear that some toys are puppets. Hence, only conclusion A follows.
 

 

Example-6

St. I—Rohan is a good swimmer.

 

St. II—Swimmers are healthy.

 

Con A—All healthy persons are swimmers.

 

Con B—Rohan is healthy.

Solution

Conclusion A is an immediate inference drawn from statement II. The term ‘healthy persons’ is distributed in this conclusion without being distributed in statement II. Hence, conclusion A does not follow.

 

Since one of the statements is particular, the conclusion should be particular (rule 6). Further, since both the statements are affirmative, the conclusion should be affirmative (rule 8).

 

Conclusion B satisfies both the above conditions and so it follows.

 

Answer: (2)
 

Analysis with Venn diagram.

 

Description: 110741.png

 

From the diagram, it is clear that Rohan is healthy. But, all healthy persons are not swimmers. Hence, only conclusion B follows.
 

 

Example-6

St. I—All keys are locks.

 

St. II—All locks are screws.

 

Con A—All screws are keys.

 

Con B—Some locks are keys.

Solution

The term ‘screws’ is distributed in conclusion A without being distributed in any of the premises. So conclusion A does not follow (rule 1). Conclusion B is an immediate inference drawn from premise I and it follows.

 

Answer: (2)
 

Analysis with Venn diagram.

 

Description: 110757.png

 

From the diagram, it is clear that all screws are not keys, but some locks are keys. Hence, only conclusion B follows.
 

 

Example-7

St. I—50% tourists carry their belongings in suitcases.

 

St. II—50% carry airbags.

 

Con A—Every tourist carries either suitcase or airbag.

 

Con B—Some tourists carry both.

Solution

If any of the tourist is not carrying both suitcase and airbag, conclusion A follows. If some tourists carry both suitcase and airbag, conclusion B follows. So, either conclusion A or conclusion B follows.

 

Answer: (3)
 

Analysis with Venn diagram.

 

 

 

In diagram 1, some tourists are carrying both suitcase and air bag.

 

In diagram 2, every tourist carries either suitcase or airbag.

 

These are the only two possibilities and only one of them can be true at a time. Both of them cannot be true simultaneously. Similarly, both of them cannot be false simultaneously. Hence, either conclusion A or conclusion B follows.
 

 

Example-8

St. I—Doctors married only fair girls.

 

St. II—Sushma is very fair.

 

Con A—Sushma was married to a doctor.

 

Con B—Sushma was not married to a doctor.

Solution

The above data does not mention whether all fair girls were married to doctors. So, either of the two conclusions may follow.

 

Answer: (3)
 

Analysis with Venn diagram.

 

Description: 110779.png

 

From the above diagrams, we notice that either conclusion A or conclusion B follows.
 





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