Examine the following statements:
I. All children are inquisitive.
II. Some children are inquisitive.
III. No

Question

Examine the following statements:
I. All children are inquisitive.
II. Some children are inquisitive.
III. No children are inquisitive.
IV. Some children are not inquisitive.
Among these statements, the two statements which cannot both be true simultaneously but can both be false would be

Accepted Answer

The correct answer is A because of the relationship between contrary statements in formal logic.

Statement I is a Universal Affirmative (All children are inquisitive) and Statement III is a Universal Negative (No children are inquisitive).

In logic, these two statements are called contraries. They cannot both be true at the same time because one claims every child has the quality while the other claims no child has it. However, they can both be false if some children are inquisitive and some are not.

For example, if in reality 50 percent of children are inquisitive, then the statement All children are inquisitive is false, and the statement No children are inquisitive is also false. Thus, they fulfill the criteria of being unable to be true together but capable of being false together.

Answer

I and III

Answer

I and IV

Answer

II and III

Answer

III and IV

Examine the following statements: I. All children are inquisitive. II. Some children are inquisitive. III. No children are inquisitive. IV. Some children are not inquisitive. Among these statements, the two statements which cannot both be true simultaneously but can both be false would be

Explanation

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