If (p wedge sim q) wedge (p wedge r) rightarr | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The implication $A \rightarrow B$ is false only when $A$ is true and $B$ is false.Given $(p \wedge \sim q) \wedge (p \wedge r) \rightarrow \sim p

Vedclass · Accepted Answer

$T, F, T$

Vedclass · Answer

(C) The implication $A \rightarrow B$ is false only when $A$ is true and $B$ is false.Given $(p \wedge \sim q) \wedge (p \wedge r) \rightarrow \sim p \vee q \equiv F$.This implies $(p \wedge \sim q) \wedge (p \wedge r) \equiv T$ and $\sim p \vee q \equiv F$.From $\sim p \vee q \equiv F$,we get $\sim p \equiv F$ and $q \equiv F$,which means $p \equiv T$ and $q \equiv F$.Now substitute these into the first part: $(T \wedge \sim F) \wedge (T \wedge r) \equiv T$.$(T \wedge T) \wedge (T \wedge r) \equiv T$.$T \wedge (T \wedge r) \equiv T$.This requires $T \wedge r \equiv T$,which implies $r \equiv T$.Thus,the truth values are $p = T, q = F, r = T$.

If $(p \wedge \sim q) \wedge (p \wedge r) \rightarrow \sim p \vee q$ is false,then the truth values of $p, q$ and $r$ are respectively

Similar Questions

The compound statement $(P \vee Q) \wedge (\sim P) \Rightarrow Q$ is equivalent to:

The statement $(p \wedge \sim q) \wedge (\sim p \vee q)$ is a...

For statements $p$ and $q$,which of the following is true?

Which of the following statements is/are False?
$S_1: \exists n \in N$, such that $n^2 + n + 2$ is divisible by $4$.
$S_2: \exists x \in N$, such that $x - 17 < 20$.
$S_3: \forall n \in N, x^2 + 3x - 10 = 0$.
$S_4: \forall n \in N, n^2 \ge 1$.

Which of the following statements is $NOT$ logically equivalent to $(p \to \sim p) \to (p \to q)$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module