If the truth value of the compound statement | vedclass

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

Question

(C) The implication $A 	o B$ is $False$ only when $A$ is $True$ and $B$ is $False$.Here, $A = (p \lor q) \land (q 	o r) \land (\sim r)$ and $B = (p

Vedclass · Accepted Answer

$(F, T)$

Vedclass · Answer

(C) The implication $A 	o B$ is $False$ only when $A$ is $True$ and $B$ is $False$.Here, $A = (p \lor q) \land (q 	o r) \land (\sim r)$ and $B = (p \land q)$.For $A$ to be $True$, all components must be $True$: $(p \lor q) = T$, $(q 	o r) = T$, and $(\sim r) = T$.From $(\sim r) = T$, we get $r = F$.Since $(q 	o r) = T$ and $r = F$, $q$ must be $F$ (because $T 	o F$ is $F$).Since $(p \lor q) = T$ and $q = F$, $p$ must be $T$.Now, check $B = (p \land q) = (T \land F) = F$. This matches the condition.Thus, $p = T$ and $q = F$.Now, $p 	o q = T 	o F = F$ and $q 	o p = F 	o T = T$.The truth values are $(F, T)$.

If the truth value of the compound statement $[(p \lor q) \land (q \to r) \land (\sim r)] \to (p \land q)$ is $False$, then the truth values of $p \to q$ and $q \to p$ are respectively...

Similar Questions

If $p$ and $q$ each have truth value $F$,then the truth values of the statement patterns $(\sim p \vee q) \leftrightarrow \sim(p \wedge q)$ and $\sim p \leftrightarrow (p \rightarrow \sim q)$ respectively are

The negation of the statement "If India wins the match,then India will reach the final" is:

Which of the following is a contradiction?

Given the following two statements:
$(S_{1}): (q \vee p) \rightarrow (p \leftrightarrow \sim q)$ is a tautology.
$(S_{2}): \sim q \wedge (\sim p \leftrightarrow q)$ is a fallacy.
Then:

The contrapositive of the converse of $p \Rightarrow q$ is......

Vedclass Test Series

Exam Paper Generator

Online Exam Module