Question

If a population consists of 50% men, then 50% of the population must be women. Is this the contrapositive statement: If a population does not consist of 50% women, then the population does not consist of 50% men.

a. True
b. False

Answer 1

The statement provided is the correct contrapositive of the original statement, which follows the format 'If not Q, then not P', making the statement True.

Step-by-step explanation:

The student has asked whether the statement 'If a population does not consist of 50% women, then the population does not consist of 50% men' is the contrapositive of the statement 'If a population consists of 50% men, then 50% of the population must be women'. The answer to this is True. The contrapositive of a conditional statement is formed by negating both the hypothesis and conclusion of the original statement and then reversing them. So, the contrapositive of 'If P, then Q' would be 'If not Q, then not P'. In this case, P is 'the population consists of 50% men' and Q is 'the population consists of 50% women'. Therefore, the contrapositive statement provided by the student is indeed correct.