First slide

Introduction to mathematical reasoning

Question

If $p \Rightarrow (q \lor r)$ is false, then truth values of p,q,r are respectively

Easy

A

T, T, F
B

T,F,F
C

F, F, F
D

F,T,T

Solution

Given statement $p \Rightarrow (q \lor r)$ is false.
$∵ p \to (q \lor r) = (~ p) \lor (q \lor r)$
Now, by trial and error method, if truth value of p is T,
q is F and r is F, then truth value of $(q \lor r)$ is F.
So, truth value of $[(~ p) \lor (q \lor r)]$ is false.
Thus, if truth value of p, e, r are T, F, F, then the
statement $p \to (q \lor r)$ is false

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