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, $A = [(p \leftrightarrow q) \land (q 	o r) \land \sim r]$ is $T$ and $B = (p \land \sim q)$ is $F$.Step $3$: From $A = T$, we get $(p \leftrightarrow q) = T$, $(q 	o r) = T$, and $\sim r = T$ (so $r = F$).Step $4$: Since $r = F$ and $(q 	o r) = T$, $q$ must be $F$ (because $F 	o F$ is $T$).Step $5$: Since $q = F$ and $(p \leftrightarrow q) = T$, $p$ must be $F$ (because $F \leftrightarrow F$ is $T$).Step $6$: Check $B = (p \land \sim q) = (F \land \sim F) = (F \land T) = F$. This matches our condition.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

The logical equivalent of $p \Leftrightarrow q$ is :-

Given the statement: "If you live in Delhi,then you have winter clothes."
Identify the following statements as contrapositive or converse of the given statement:
$(i)$ If you do not have winter clothes,then you do not live in Delhi.
$(ii)$ If you have winter clothes,then you live in Delhi.

Verify by the method of contradiction.
$p: \sqrt{7}$ is irrational

The statement $p$ $\rightarrow (q$ $\rightarrow p)$ is equivalent to

Find the component statements of the following and check whether they are true or not.
$\sqrt{2}$ is a rational number or an irrational number.

Vedclass Test Series

Exam Paper Generator

Online Exam Module