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 $1$: Analyze the given implication $[(p \leftrightarrow q) \land (q 	o r) \land \sim r] 	o (p \land \sim q) = F$. An implication is false o

Vedclass · Accepted Answer

$(T, F)$

Vedclass · Answer

(B) Step $1$: Analyze the given implication $[(p \leftrightarrow q) \land (q 	o r) \land \sim r] 	o (p \land \sim q) = F$. An implication is false only when the antecedent is $T$ and the consequent is $F$.Step $2$: Consequent $(p \land \sim q) = F$. Antecedent $[(p \leftrightarrow q) \land (q 	o r) \land \sim r] = T$. This implies $(p \leftrightarrow q) = T$, $(q 	o r) = T$, and $\sim r = T$.Step $3$: From $\sim r = T$, we get $r = F$. Since $(q 	o r) = T$ and $r = F$, $q$ must be $F$. Since $(p \leftrightarrow q) = T$ and $q = F$, $p$ must be $F$.Step $4$: Evaluate the first pattern $(p 	o q) \leftrightarrow (q 	o r)$. Substituting $p=F, q=F, r=F$: $(F 	o F) \leftrightarrow (F 	o F) \equiv T \leftrightarrow T = T$.Step $5$: Evaluate the second pattern $\sim (p \lor r) 	o (q \land p)$. Substituting $p=F, q=F, r=F$: $\sim (F \lor F) 	o (F \land F) \equiv \sim F 	o F \equiv T 	o F = F$.Step $6$: 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

If $(p \wedge \sim r) \Rightarrow (q \vee r)$ is false and $q$ and $r$ are both false,then $p$ is

Check whether the following sentence is a statement. Give reasons for your answer.
$8$ is less than $6.$

Consider the following statements:
$r: \text{If } p \to q \text{ is false, then } p \lor q \text{ is false.}$
$s: \text{If } p \leftrightarrow q \text{ is false, then } p \lor q \text{ is false.}$
The truth values of $r \to s$ and $s \to r$ are respectively . . . . . .

If $p$: It rains today,$q$: $I$ go to school,$r$: $I$ shall meet my friend,and $s$: $I$ shall go for a movie,then which of the following represents the proposition: "If it does not rain or if $I$ do not go to school,then $I$ shall meet my friend and go for a movie"?

Which of the following statement patterns is a contradiction?
$S_{1} \equiv (p \rightarrow q) \wedge (p \wedge \sim q)$
$S_{2} \equiv [p \wedge (p$ $\rightarrow q)]$ $\rightarrow q$
$S_{3} \equiv (p \vee q) \rightarrow \sim p$
$S_{4} \equiv [p \wedge (p \rightarrow q)] \leftrightarrow q$

Vedclass Test Series

Exam Paper Generator

Online Exam Module