Question : Directions: Three statements are given followed by four conclusions. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically does NOT follow(s) from the statements.
Statements:
I. All P is G.
II. Some G is B.
III. All B is C.
Conclusions:
I. All P being C is a possibility.
II. Some P is B.
III. Some C is G.
IV. Some G is P.
Option 1: Only III does not follow
Option 2: Only IV does not follow
Option 3: Only II does not follow
Option 4: Only I does not follow
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Correct Answer: Only II does not follow
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions –
Conclusion I:
All P being C is a possibility – It is a possibility that the circle representing P is completely overlapped by the circle representing C. Thus, this conclusion follows.
Conclusion II:
Some P is B – From the Venn diagram, it is evident that there is no direct relation between P and B. So, no definite relation can be drawn. Thus, this conclusion does not follow.
Conclusion III:
Some C is G – From the Venn diagram, it is evident that the circles representing C and G overlap and have some parts of their area in common. So, from this, it can be concluded that some C is G. Thus, this conclusion follows.
Conclusion IV:
Some 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 follows.
So, only conclusion II does not follow. Hence, the third option is correct.
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