Determine the statement that is logically equivalent to this conditional statement. If there is a thunderstorm, the lake floods.

This question lacks options, the options are:

A) If the lake does not flood, there is a thunderstorm.

B) If the lake floods, then there is not a thunderstorm.

C) If there is not a thunderstorm, the lake does not flood.

D) If the lake does not flood, then there is not a thunderstorm.

The correct answer is D

Explanation:

A conditional statement is a statement whose effect is dependent on another, it is usually recognized with the IF word. A Contrapositive of an original conditional statement, is the inverse of the converse of an original statement that doesn't change the meaning of the original statement.

For example; A -> B is the original conditional statement

Converse is B -> A

The Contrapositive is (not B -> not A)

The original conditional statement is: If there is a thunderstorm, the lake floods.

(This means that there is flooding of the lake in the presence of a thunderstorm)

The contrapositive of this statement is:

If the lake does not flood, then there is not a thunderstorm.

(This retains the meaning of the original statement. It means that the absence of a flood certainly means the absence of a thunderstorm)

Since the contrapositive is logically equivalent to the conditional statement, then the option D is the logically equivalent to the conditional statement.

Note: Option C is wrong because other factors might cause flooding of the lake, so the absence of thunderstorm doesn't mean there'll be no flooding of the lake but no flooding certainly means no thunderstorm, which option D is portraying.

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