Question

write the converse, inverse, and contrapositive of the true conditional statement. determine whether the related conditional is true or false.
air travel ulma is waiting to board an airplane. over the speakers she hears a flight attendant say \if you are seated in rows 10 to 20, you may now board.\
converse: select choice ↓, then select choice ↓. the converse is select choice ↓. inverse: if you select choice ↓ seated in rows 10 to 20, then you may not board now. the inverse is select choice ↓. contrapositive: if you are not allowed to board now, then you select choice ↓ seated in rows 10 to 20. the contrapositive is select choice ↓.

Explanation:

Step1: Identify the original conditional

Let the original conditional be \( p \to q \), where \( p \): "you are seated in rows 10 to 20", \( q \): "you may now board".

Step2: Find the converse

Converse: \( q \to p \), so "If you may now board, then you are seated in rows 10 to 20". This is false because there could be other rows allowed to board now.

Step3: Find the inverse

Inverse: \(
eg p \to
eg q \), so "If you are not seated in rows 10 to 20, then you may not board now". This is false because other rows might be allowed to board.

Step4: Find the contrapositive

Contrapositive: \(
eg q \to
eg p \), so "If you may not board now, then you are not seated in rows 10 to 20". This is true because the original statement implies that only rows 10 - 20 can board now, so if you can't board, you aren't in those rows.

Answer:

• Converse: If you may now board, then you are seated in rows 10 to 20 (False)
• Inverse: If you are not seated in rows 10 to 20, then you may not board now (False)
• Contrapositive: If you may not board now, then you are not seated in rows 10 to 20 (True)