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(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

$(F, T)$

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(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

Consider the following statements:
Statement $I$: If a quadrilateral $ABCD$ is a square,then all of its sides are equal.
Statement $II$: If all the sides of a quadrilateral $ABCD$ are equal,then $ABCD$ is a square.
Then:

Consider the statement patterns:
$A. (q \to p) \lor (p \to q)$
$B. (\sim p \lor \sim q) \leftrightarrow \sim (p \land q)$
$C. [(p \lor q) \land \sim p] \land \sim q$
$D. (p \land q) \land (\sim p \lor \sim q)$
Then identify the nature of these statement patterns.

The negation of the statement "If an integer is greater than $4$ and less than $5$, then it is a multiple of $3$" is:

Find the function $f(x_{1}, x_{2}, x_{3})$ that satisfies $f(x_{1}, x_{2}, x_{3}) = 1$ at $x_{1} = 1, x_{2} = 0, x_{3} = 0$.

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