Question

example 5 write the converse, inverse, and contrapositive of each true conditional statement. determine whether each related conditional is true or false. if a statement is false, then find a counterexample. 18. 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.” 19. raffle if you have five dollars, then you can buy five raffle tickets. 20. geometry if two angles are complementary, then the angles are acute. 21. medication a medicine bottle says “if you will be driving, then you should not take this medicine.”

Explanation:

18.

• Conditional statement: If you are seated in rows 10 to 20, you may now board.
• Converse: If you may now board, then you are seated in rows 10 to 20. False. Counter - example: There could be pre - boarding for first - class passengers or passengers with special needs who are not in rows 10 - 20.
• Inverse: If you are not seated in rows 10 to 20, then you may not now board. False. Counter - example: The same pre - boarding cases as above.
• Contrapositive: If you may not now board, then you are not seated in rows 10 to 20. True

19.

• Conditional statement: If you have five dollars, then you can buy five raffle tickets.
• Converse: If you can buy five raffle tickets, then you have five dollars. True (assuming the price of each raffle ticket is one dollar and no other payment methods are available)
• Inverse: If you do not have five dollars, then you cannot buy five raffle tickets. True
• Contrapositive: If you cannot buy five raffle tickets, then you do not have five dollars. True

20.

• Conditional statement: If two angles are complementary, then the angles are acute.
• Converse: If two angles are acute, then they are complementary. False. Counter - example: Two angles of 30° and 40° are acute but their sum is 70°≠90°, so they are not complementary.
• Inverse: If two angles are not complementary, then the angles are not acute. False. Counter - example: Two angles of 10° and 80° are acute but not complementary.
• Contrapositive: If two angles are not acute, then they are not complementary. True

21.

• Conditional statement: If you will be driving, then you should not take this medicine.
• Converse: If you should not take this medicine, then you will be driving. False. Counter - example: You may not be able to take the medicine because of other health conditions even if you are not driving.
• Inverse: If you will not be driving, then you should take this medicine. False. Counter - example: There could be other reasons like allergies or contra - indications for taking the medicine.
• Contrapositive: If you should take this medicine, then you will not be driving. True

Answer:

18.

• Conditional statement: If you are seated in rows 10 to 20, you may now board.
• Converse: If you may now board, then you are seated in rows 10 to 20. False. Counter - example: There could be pre - boarding for first - class passengers or passengers with special needs who are not in rows 10 - 20.
• Inverse: If you are not seated in rows 10 to 20, then you may not now board. False. Counter - example: The same pre - boarding cases as above.
• Contrapositive: If you may not now board, then you are not seated in rows 10 to 20. True

19.

• Conditional statement: If you have five dollars, then you can buy five raffle tickets.
• Converse: If you can buy five raffle tickets, then you have five dollars. True (assuming the price of each raffle ticket is one dollar and no other payment methods are available)
• Inverse: If you do not have five dollars, then you cannot buy five raffle tickets. True
• Contrapositive: If you cannot buy five raffle tickets, then you do not have five dollars. True

20.

• Conditional statement: If two angles are complementary, then the angles are acute.
• Converse: If two angles are acute, then they are complementary. False. Counter - example: Two angles of 30° and 40° are acute but their sum is 70°≠90°, so they are not complementary.
• Inverse: If two angles are not complementary, then the angles are not acute. False. Counter - example: Two angles of 10° and 80° are acute but not complementary.
• Contrapositive: If two angles are not acute, then they are not complementary. True

21.

• Conditional statement: If you will be driving, then you should not take this medicine.
• Converse: If you should not take this medicine, then you will be driving. False. Counter - example: You may not be able to take the medicine because of other health conditions even if you are not driving.
• Inverse: If you will not be driving, then you should take this medicine. False. Counter - example: There could be other reasons like allergies or contra - indications for taking the medicine.
• Contrapositive: If you should take this medicine, then you will not be driving. True