Question

If p, q, r are simple propositions with truth values T, F, T, then the truth value of $(\sim p \vee q)\mspace{6mu} \land \sim r \Rightarrow p$ is

• A. True
• B. False
• C. True if r is false
• D. True if q is true

Answer 1

Answer: (A)

True

Answer 2

$\sim p \vee q$ means F$\vee$F = F, ~r means F$(\sim p \vee q) \land \sim r$ means F

$\because\lbrack(\sim p \vee q)\mspace{6mu} \land \sim r\rbrack \Rightarrow p$ means T

[$\because$in $p \Rightarrow q$ we have FTT]