Understanding the Inverse of a Conditional Statement

What is the inverse of the following conditional statement?

If you spill your drink, then the carpet will get stained.

A. If you do not spill your drink, then the carpet will not get stained.

B. If the carpet is stained, then you must have spilled your drink.

C. The carpet will get stained if and only if you spill your drink.

Answer:

Option A. If you do not spill your drink, then the carpet will not get stained.

The inverse of a conditional statement negates both the condition and the result. In this case, the inverse of the statement 'If you spill your drink, then the carpet will get stained' is 'If you do not spill your drink, then the carpet will not get stained,' which corresponds to Option A.

Explanation:

The inverse of a conditional statement switches the hypothesis and the conclusion, and then negates both. If the original conditional is 'If you spill your drink, then the carpet will get stained,' the inverse would negate both the condition and the result. So, 'if you do not spill your drink, then the carpet will not get stained' would be the correct inverse. Therefore, Option A is the correct answer. Option B represents the converse, which only switches the hypothesis and conclusion without negating. Option C represents the biconditional, which states the condition and result can only occur together.