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.”


Which option is true?
Both Meg and Cassandra are incorrect.

Only Meg is correct.

Both Meg and Cassandra are correct.

Only Cassandra is correct.

Answer 1

OK, so final answer: p=stuck in traffic, q=late, 1)p-->q 2)q-->p 3)-q-->-p.

Meg says 3 is inverse of 2 and contrapositive of 1. This is correct, because inverse of 2 is -q-->-p and contrapositive of 1 is -q-->-p.

Cassandra says 2 is converse of 1 and inverse of 3. That is correct, because converse of 1 is q-->p and inverse of 3 is --q-->--p which is logically equivalent to q-->p.

Answer 2

So both are correct.