Question 2(Multiple Choice Worth 1 points)

(01.05 MC)

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.

1 answer

To analyze the statements and determine who is correct, we need to look at the definitions of converse, inverse, and contrapositive.

  1. Statement 1: "If she is stuck in traffic (p), then she is late (q)."

    • Converse of Statement 1: "If she is late (q), then she is stuck in traffic (p)." (This is Statement 2)
    • Inverse of Statement 1: "If she is not stuck in traffic (not p), then she is not late (not q)."
    • Contrapositive of Statement 1: "If she is not late (not q), then she is not stuck in traffic (not p)."
  2. Statement 2: "If she is late, then she is stuck in traffic."

    • This is the converse of Statement 1.
  3. Statement 3: "If she is not late, then she is not stuck in traffic."

    • This is the inverse of Statement 1, not the contrapositive.

Now let's evaluate Meg's and Cassandra's claims:

  • Meg's claim: "Statement 3 is the inverse of statement 2 and contrapositive of statement 1."

    • Statement 3 is not the inverse of Statement 2. Statement 2 is the converse of Statement 1. Statement 3 is the inverse of Statement 1, not the contrapositive.
  • Cassandra's claim: "Statement 2 is the converse of statement 1 and the inverse of statement 3."

    • Statement 2 is indeed the converse of Statement 1, but it is not the inverse of Statement 3. Statement 3 has a different relationship with Statement 1, as stated above.

From this analysis, we conclude that:

  • Meg is incorrect about both parts of her statement.
  • Cassandra is correct about the first part of her statement but incorrect about the second part.

Therefore, the answer is Only Meg is correct.