Question

If $p,q,r$ are simple propositions with truth values $T,F,T$ then the truth value $(~p\vee q)\wedge ~r\Rightarrow p$ is

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

Answer 1

The correct option is A

True

Explanation for the correct option

Lets examine the LHS of the expression $(~p\vee q)\wedge ~r\Rightarrow p$

Now the truth value for $p$ true then $~p$ is F and the truth value for $q$ is F then,

$(~p\vee q)$ means $F\vee F=F$

Then, we have the truth value of $r$ as T

Therefore, the statement $~r$ is $F$

This implies that $(~p\vee q)\wedge ~r=F\wedge F$ which is equal to $F$

Now $(~p\vee q)\wedge ~r\Rightarrow p$ is $F\Rightarrow T$ which is means $T$

Therefore, truth value of the given statement is True

Hence, option (A) is the correct answer.