To analyze the statements and determine who is correct, we need to look at the definitions of converse, inverse, and contrapositive.
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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)."
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Statement 2: "If she is late, then she is stuck in traffic."
- This is the converse of Statement 1.
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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:
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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.
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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.
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