Question : Directions: Three statements are given, followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
All c is f.
No f is t.
All p is c.
Conclusions:
I. Some t is c.
II. No p is t.
Option 1: Only conclusion II follows
Option 2: Only conclusion I follows
Option 3: Neither conclusion I nor II follows
Option 4: Either conclusion I or II follows
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Correct Answer: Only conclusion II follows
Solution : The possible Venn diagram, according to the given statements is as follows –
Let's analyse the conclusions –
Conclusion (I):
Some t is c – From the Venn diagram, it is evident that all c is f and no f is t. So, it can be concluded that no c is t. Therefore, this conclusion does not follow.
Conclusion (II):
No p is t – From the Venn diagram, it is evident that all p is c, all c is f and no f is t. So, it can be concluded that no p is t.
So, the only conclusion II follows. Hence, the first option is correct.
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