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.\

who is correct?

both meg and cassandra are incorrect.
only meg is correct.
both meg and cassandra are correct.
only cassandra is correct.

Explanation:

Define the logical statements

Using Conditional Logic, let:

• \(p\): "she is stuck in traffic"
• \(q\): "she is late"

The statements are:

• Statement 1: \(p

ightarrow q\)

• Statement 2: \(q

ightarrow p\)

• Statement 3: \(

eg q
ightarrow
eg p\)

Analyze Meg's claim

Meg claims Statement 3 is:

• The inverse of Statement 2: The inverse of Statement 2 (\(q

ightarrow p\)) is \(
eg q
ightarrow
eg p\), which is Statement 3. This is correct.

• The contrapositive of Statement 1: Using Contrapositive Statement, the contrapositive of Statement 1 (\(p

ightarrow q\)) is \(
eg q
ightarrow
eg p\), which is Statement 3. This is correct.

Thus, Meg is correct.

Analyze Cassandra's claim

Cassandra claims Statement 2 is:

• The converse of Statement 1: Using Converse Statement, the converse of Statement 1 (\(p

ightarrow q\)) is \(q
ightarrow p\), which is Statement 2. This is correct.

• The inverse of Statement 3: The inverse of Statement 3 (\(

eg q
ightarrow
eg p\)) is \(
eg(
eg q)
ightarrow
eg(
eg p)\), which simplifies to \(q
ightarrow p\) (Statement 2). This is correct.

Thus, Cassandra is correct.

Determine the final correct option

Since both Meg and Cassandra are correct, the correct choice is "Both Meg and Cassandra are correct."

Answer:

• Both Meg and Cassandra are incorrect.
• Only Meg is correct.
• Both Meg and Cassandra are correct. (Correct answer)
• Only Cassandra is correct.