Question

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."

Karen writes, "Statement 2 is the converse of statement 3 and contrapositive of statement 1."
Laura writes, "Statement 2 is the converse of statement 1 and inverse of statement 3."

Answer 1

Which option is true?

Both Karen and Laura are incorrect.

Only Laura is correct.

Both Karen and Laura are correct.

Only Karen is correct.

Answer 2

ONLY LAURA IS CORRECT

Answer 3

Only laura is correct

Answer 4

That's what I thought it would be. Thanks :)

Answer 5

:)

Answer 6

Laura is correct because
Let P = she is stuck in traffic
Let Q = she is late

Statement 1: "If she is stuck in traffic, then she is late." \(P\rightarrow Q\)
Statement 2: "If she is late, then she is stuck in traffic." \(Q\rightarrow P\)
Statement 3: "If she is not late, then she is not stuck in traffic." \(\neg P\rightarrow \neg Q\)

Karen says "Statement 2 is the converse of statement 3 and contrapositive of statement 1."
In other words, she says that Statement 2 is logically \(\neg P \rightarrow \neg Q\) and \(\neg Q \rightarrow \neg P\) which means that "She is not late iff she is not stuck in traffic", which is not what statement 2 means, logically.

Laura says "Statement 2 is the converse of statement 1 and inverse of statement 3."
In other words, she says that Statement 2 logically \( Q \rightarrow P\) and \( Q \rightarrow P\), which are ,of course, the same and is logically true.

Answer 7

*Statement 3 should be \(\neg Q \rightarrow \neg P\), everything else is correct.

Answer 8

That helped me understand it a lot more .

Answer 9

Thank you.