First slide

Introduction to mathematical reasoning

Question

If each of the statements $p \to\sim q, ~ r \to q$ and p are true, then which of the following is NOT true?

Moderate

A

q is false
B

r is true
C

$r \to q$ is false
D

$r \land ~ q$ is false

Solution

Since p is true and $p \to\sim q$ is also true, therefore $~ q$ is true.
Also, since $~ r \to q$ is true, $∼r$ is false and so, r is true.
From above $r \to q$ is false.

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