Question : Directions: Three statements are given followed by four conclusions numbered 1, 2, 3, and 4. 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:
All K are S.
No S is a B.
Some B are T.
Conclusions:
1) No K are B.
2) Some T are not S.
3) Some T are B.
4) All B being K is a possibility.
Option 1: Only 2 does not follow
Option 2: Only 1 does not follow
Option 3: Only 3 does not follow
Option 4: Only 4 does not follow
Correct Answer: Only 4 does not follow
Solution : According to the given statements, the Venn diagram is as follows –
Let us analyse the conclusions –
Conclusion 1:
No K are B – Since all K are S and no S is B. Therefore, no K will be B. Thus, this conclusion follows.
Conclusion 2:
Some T are not S – Since some T is B. Therefore, some T will not be S as no S is B. Thus, this conclusion follows.
Conclusion 3:
Some T are B – From the Venn diagram, it is evident that the circles representing B and T overlap and have a part of their area in common. Thus, it can be concluded that some T are B.
Conclusion 4:
All B being K is a possibility – Since all K are S and no S is B. Therefore, no B can be a K. Thus, this conclusion does not follow.
So, only conclusion 4 does not follow. Hence, the fourth option is correct.