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.

Answer 1

Both Meg and Cassandra are correct.

Meg correctly identifies that statement 3 is the inverse of statement 2 and the contrapositive of statement 1. The inverse of a statement is formed by negating both the hypothesis and the conclusion of the original statement. The contrapositive of a statement is formed by negating both the hypothesis and the conclusion and then reversing the order.

Cassandra correctly identifies that statement 2 is the converse of statement 1 and the inverse of statement 3. The converse of a statement is formed by reversing the order of the hypothesis and the conclusion.