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Question

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



Correct Answer
A

True

Your Answer
B

False

Your Answer
C

May be true or false

Your Answer
D

Cannot conclude from given the information


Solution

The correct option is C

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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