Possibility Syllogism Positive Two Statement

Possibility Syllogism - Positive Two Statements:

Illustration::  In the question below, two statements are given followed by Conclusions numbered I and II. The candidate has to assume all the statements to be true even if they seem to be at variance from the commonly known facts and then decide which of the given two Conclusions logically follows from the information given in the statements and mark the option best suited.

Statement : - I. Some car are truck.

                    II.  All scooters are car.

Conclusion : - I.  Some truck being scooter is a possibility.

                       II. All cars may be scooter.

A. Only Conclusion I follows         B. Only Conclusion II follows           C. Either Conclusion I or II follows         

D. Neither Conclusion I nor II follows                            E. Both Conclusions I and II follow

Answer :  A

Solution:-  To solve these type of questions we will show the relations between the objects using a venn diagram. As in the first statement it is given that Some car are truck. It means that there are some cars which are not trucks so it is shown by an intersecting circles. Similarly the second statement it is given that all scooters are car, this relation is shown by an overlapping circle. Now there can be two possibilities as shown in the figures below

Possibility I: No Scooters are trucks. So it can be shown as disjoint circles

Possibility II: Some Scooters are trucks also. This can be shown by an intersecting circle.

For checking the possible case, it is important to first check definite case for the some conclusions. It definite case is false, possible case is true. If definite case is true, possible case is always false.

Conclusion I Some truck is a scooter : - Definite case is false as scooter and truck are not related to one another. Therefore Possible case is true.

Conclusion II All cars are scooter : - Definite case is false as all cars can never be scooter because it is mentioned that all scooters are cars. Since definite case is false, so its possible case is true.

Hence option A that is only Conclusion I follows is true.

Illustration::  In the question below, two statements are given followed by Conclusions numbered I and II. The candidate has to assume all the statements to be true even if they seem to be at variance from the commonly known facts and then decide which of the given two Conclusions logically follows from the information given in the statements and mark the option best suited.

Statement : - I.  All dogs are pets.

                     II. Some cats are dogs.

Conclusion : - I. Some cats are pet is possible.

                      II. All cats are pet is possible.

A. Only Conclusion I follows         B. Only Conclusion II follows           C. Either Conclusion I or II follows         

D. Neither Conclusion I nor II follows                            E. Both Conclusions I and II follow

Answer :  E

Solution:-  To solve these type of questions we will show the relations between the objects using a Venn Diagram. As in the first statement it is given that all dogs are pets. It is shown by an overlaping circles. and the circle representing dogs is contained in the circle representing pets. The second statement some cats are dogs can also be shown by an intersecting circle, Now there can be two possibilities as shown in the figures below

Possibility I: All cats are pets.This can be shown by overlapping circles. The circle representing cats is contained inside the circle representing pets.

Possibility II: Some cats are not pets.This can be shown by intersecting circles. The circle representing cats intersects the circle representing pets.

Conclusion I Some cats are pets : - Definitely true. So possibility false.

Conclusion II All cats are pets : - Definite case is false as we can see that some cats are pet. So possible case is true.

Hence option E that is Both Conclusions I and II follow is true.