Jose wakes up early if and only if he is going for a bike ride.
Which choice is the contrapositive of the statement?
OA Jose doesn't wake up early if and only if he isn't going for a bike ride.
OB. Jose isn't going for a bike ride if and only if he wakes up early.
OC. Jose doesn't wake up early if and only if he is going for a bike ride.
OD. Jose isn't going for a bike ride if and only if he doesn't wake up early.

Question

03-08-2022
Mathematics

Answered

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Jose wakes up early if and only if he is going for a bike ride.
Which choice is the contrapositive of the statement?
OA Jose doesn't wake up early if and only if he isn't going for a bike ride.
OB. Jose isn't going for a bike ride if and only if he wakes up early.
OC. Jose doesn't wake up early if and only if he is going for a bike ride.
OD. Jose isn't going for a bike ride if and only if he doesn't wake up early.

Sagot :

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PallasAthena23 PallasAthena23 · Answer 1 · 2022-08-03T12:37:28-04:00

A. J’ose doesn’t wake up early if and only if he isn’t going for a bike ride.

A contrapositive contradicts (goes against, is the opposite of) both the first part of the statement and then second. The first part of the statement says “Jose wakes up early”. The opposite of that would be “Jose doesn’t wake up early”. The second part of the statement says “if and only if he is going for a bike ride”. The opposite of that would be “if and only if he isn’t going for a bike ride”. So if we put this together we end up with the statement “Jose doesn’t wake up early if and only if he isn’t going for a bike ride.”

Sagot :

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