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

(B) Step $1$: The implication $A 	o B$ is false only when $A$ is $T$ and $B$ is $F$.Step $2$: Here, $A = [(p \leftrightarrow q) \land (q 	o r) \land

Vedclass · Accepted Answer

$(T, F)$

Vedclass · Answer

(B) Step $1$: The implication $A 	o B$ is false only when $A$ is $T$ and $B$ is $F$.Step $2$: Here, $A = [(p \leftrightarrow q) \land (q 	o r) \land \sim r]$ and $B = (p \land \sim q)$. Since $B$ is false, $(p \land \sim q)$ is $F$.Step $3$: Since $A$ is true, $(p \leftrightarrow q)$ is $T$, $(q 	o r)$ is $T$, and $\sim r$ is $T$. Thus, $r$ is $F$.Step $4$: Since $(q 	o r)$ is $T$ and $r$ is $F$, $q$ must be $F$ (because $T 	o F$ is $F$).Step $5$: Since $(p \leftrightarrow q)$ is $T$ and $q$ is $F$, $p$ must be $F$.Step $6$: Check consistency: $p=F, q=F, r=F$. Then $p \land \sim q = F \land T = F$. This matches $B$ being false.Step $7$: Evaluate $(p 	o q) \leftrightarrow (q 	o r)$: $(F 	o F) \leftrightarrow (F 	o F) = T \leftrightarrow T = T$.Step $8$: Evaluate $\sim (p \lor r) 	o (q \land p)$: $\sim (F \lor F) 	o (F \land F) = \sim F 	o F = T 	o F = F$.Step $9$: The truth values are $(T, F)$.

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

Similar Questions

Find the component statements of the following compound statement and check whether they are true or false.
$100$ is divisible by $3, 11$ and $5$.

If the truth value of the statement pattern $(\sim p \land q) \lor (\sim p \land \sim q) \lor (p \land \sim q)$ is $F$, then the truth values of $(p \lor \sim q)$ and $(p \to q)$ are ... respectively.

$ \sim[(\sim p) \wedge q] $ is logically equivalent to

The Boolean expression $(p \wedge q) \Rightarrow ((r \wedge q) \wedge p)$ is equivalent to:

The statement pattern $(p \lor q) \to \sim r$ is logically equivalent to

Vedclass Test Series

Exam Paper Generator

Online Exam Module