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.
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.