Please help on practice problem!!

Question

Read the following statements.

Statement 1: "If she is stuck in traffic, then she is late."

Statement 2: "If she is late, then she is stuck in traffic."

Statement 3: "If she is not late, then she is not stuck in traffic."

Meg writes, "Statement 3 is the inverse of statement 2 and contrapositive of statement 1."

Cassandra writes, "Statement 2 is the converse of statement 1 and inverse of statement 3."

Who is correct?

 Both Meg and Cassandra are incorrect. 

Only Meg is correct. 

Both Meg and Cassandra are correct.

 Only Cassandra is correct. I say option 3 but I am not sure please correct me

Answer 1

You are correct that both Meg and Cassandra are correct. An inverse of a statement is formed by negating both sides, so statements 2 and 3 are inverses of each other. A converse of a statement is formed by switching the hypothesis and conclusion, so statements 1 and 2 are converses. Finally, a contrapositive of a statement is formed by negating both sides and switching the hypothesis and conclusion, so statements 1 and 3 are contrapositives.