Question : Directions: In the following question below are given some statements followed by some conclusions based on those statements. Taking the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows the given statements.
Statements:
I. All P is G.
II. Some F is P.
Conclusions:
I. All G is P.
II. All P is F.
III. Some F is not G.
Option 1: Only conclusion III follows
Option 2: Both conclusions II and III follow
Option 3: All conclusions follow
Option 4: None of the conclusions follows
Correct Answer: None of the conclusions follows
Solution : The possible Venn diagram according to the given statement is as follows –
Let's analyse the conclusions –
Conclusion I:
All G is P – From the Venn diagram, it is evident that some parts of the circle representing G lie inside the circle representing P while some lie outside. So, from this, it can be concluded that some G is P. Thus, this conclusion does not follow.
Conclusion II:
All P is F – From the Venn diagram, it is evident that the circles representing P and F overlap and have some parts of their area in common. So, from this, it can be concluded that some P is F. Thus, this conclusion does not follow.
Conclusion III:
Some F is not G – It is a possibility that some parts of the circle representing F are not overlapped by the circle representing G. But this is not definite. Thus, this conclusion does not follow.
So, none of the conclusions follows. Hence, the fourth option is correct.
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