2 years, 2 months ago
Are p -->(q -->r) and (p-->q) --> r logically equivalent?
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M$1 Answer
You have to make the truth table T means true F means false
p ..... T T T T F F F F
q ...... T T F F T T F F
r ....... T F T F T F T F
q-->r .... T F T F T F F T
p->(q->r) . T F T F T T T T
Now do the same table for (p-->q) --> r and see if you got the same final results
Note that T-->T is T
T--->F is F
F-->T is T
F-->F is T
because from false sentences, you can obtain any answers, either true or false.
p ..... T T T T F F F F
q ...... T T F F T T F F
r ....... T F T F T F T F
q-->r .... T F T F T F F T
p->(q->r) . T F T F T T T T
Now do the same table for (p-->q) --> r and see if you got the same final results
Note that T-->T is T
T--->F is F
F-->T is T
F-->F is T
because from false sentences, you can obtain any answers, either true or false.
You can leave an optional "tip" with Mahalo's virtual currency, Mahalo Dollars. If you are asking a difficult question that might require some research, or if you'd like a wide variety of feedback, a higher tip often leads to more answers to your question.
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