Question

In the following question, examine the given statements carefully and find out which two of the statements can not be true simultaneously, but can both be false.

• A. All children are inquisitive.
• B. Some children are inquisitive.
• C. No children are inquisitive.
• D. Some children are not inquisitive. \textbf{Options:}

Hint:

When examining logical statements for contradictions, look for pairs that directly oppose each other in meaning.

Answer 1

The Correct Option is A

We are given the following statements:
% Option (1) All children are inquisitive.
% Option (2) Some children are inquisitive.
% Option (3) No children are inquisitive.
% Option (4) Some children are not inquisitive.
Step 1: Analyzing contradictions
% Option (1) and (3) are direct contradictions. If all children are inquisitive, then no children can be inquisitive. Thus, both cannot be true simultaneously.
% Option (2) and (3) are also contradictory. "Some children are inquisitive" and "No children are inquisitive" cannot both be true at the same time, but both can be false if there is some degree of inquisitiveness among children.
% Option (1) and (4) are not contradictory. It is possible for all children to be inquisitive, and still some children may not be inquisitive in some context.
Step 2: Conclusion The pair that cannot be true simultaneously, but can both be false, is (1) and (3). Therefore, the correct answer is (1).