First slide

Introduction to mathematical reasoning

Question

If p, q are true statements and r, s are false statements, then the truth value of $~ ((p \land ~ r) \lor (~ q \lor s))$ is

Easy

A

true
B

false
C

false for any p
D

None of these

Solution

$\begin{array}{ll} ~ ((T \land ~ F) \lor (~ T \lor F)) \\ \Rightarrow \equiv\sim ((T \land T) \lor (F \lor F)) \\ \Rightarrow \equiv\sim ((T) \lor (F)) \equiv\sim (T) \equiv F \end{array}$

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