Question

I don't completely understand:
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

Hints:

Let's say the original conditional statement is "If P, then Q"
Where P and Q are statements.


The converse is "If Q, then P"
The inverse is "If not P, then not Q"
The contrapositive is "If not Q, then not P"

Answer 2

Okay so,
original- if she's stuck in traffic, then she is late
converse- is the converse the same as the original ?
inverse- if shes not stuck in traffic, then she's not late
contrapositive- if shes not late, then shes not stuck in traffic

Answer 3

original- if she's stuck in traffic, then she is late

that is correct

Answer 4

converse: if she's late, then she's stuck in traffic

notice how I swapped the two ( going from "If P, then Q" to "if Q, then P")

Answer 5

inverse: if she's not stuck in traffic, then she's not late

just negate each part (ie, make it the opposite)

Answer 6

and finally,

contrapositive: if she's not late, then she's not stuck in traffic

so you swap and you negate each part