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Question

If (pr)(q r) is false and q and r are both false, then p is ___.


A

True

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B

False

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C

May be true or false

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D

Cannot conclude from given the information

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Solution

The correct option is A

True


pq is false only when p is true and q is false.
Given that (p r)(q r) is false.
Hence, p r is true and q r is false.

Given that q and r are both false. Hence, q r is false.
Since r is false, r is true.
p r must be true. Hence, p must be true.


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