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

(A) conditional statement $A 	o B$ 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 = (

Vedclass · Accepted Answer

$(F, T)$

Vedclass · Answer

(A) conditional statement $A 	o B$ is false only when $A$ is true and $B$ is false.Here, $A = [(p \lor q) \land (q 	o r) \land (\sim r)]$ and $B = (p \land q)$.Since $B = (p \land q)$ is false, at least one of $p$ or $q$ must be false.Since $A$ is true, all components $(p \lor q)$, $(q 	o r)$, and $(\sim r)$ must be true.From $(\sim r) = T$, we get $r = F$.Substitute $r = F$ into $(q 	o r) = T$, which becomes $(q 	o F) = T$. This implies $q = F$.Now substitute $q = F$ into $(p \lor q) = T$, which becomes $(p \lor F) = T$. This implies $p = T$.Check consistency: $p=T, q=F, r=F$. $B = (T \land F) = F$ (Correct).Now calculate truth values:$p 	o q = T 	o F = F$.$q 	o p = F 	o T = T$.Thus, 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

Negation of the statement $(p \vee r) \Rightarrow (q \vee r)$ is :

The dual of the statement pattern $(p \land \sim q) \to (q \land \sim p)$ is equivalent to

$p \Rightarrow q$ can also be written as

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

Let $A, B, C$ and $D$ be four non-empty sets. The contrapositive statement of "If $A \subseteq B$ and $B \subseteq D,$ then $A \subseteq C$" is

Vedclass Test Series

Exam Paper Generator

Online Exam Module