First slide

Introduction to mathematical reasoning

Question

If $(p \land ~ r) \to (~ p \lor q)$ is false, then truth values of p, q and r are, respectively,

Moderate

A

T, T, T
B

T, F, T
C

T, F, F
D

F, T, T

Solution

$(p \land ~ r) \to (~ p \lor q)$ is false.
Thus, $(p \land ~ r)$ is true and $(~ p \lor q)$ is false
So, (p is true and $~ r$ is true) and ( $~ p$ is false and g is false)
Therefore, p is true, r is false and q is false.

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