If q is false and p wedge q leftrightarrow r | vedclass

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(B) Given that $q$ is false and $p \wedge q \leftrightarrow r$ is true.Since $q \equiv F$,then $p \wedge q \equiv F$.For the biconditional $p \wedge q

Vedclass · Accepted Answer

$(p \wedge r) \rightarrow (p \vee r)$

Vedclass · Answer

(B) Given that $q$ is false and $p \wedge q \leftrightarrow r$ is true.Since $q \equiv F$,then $p \wedge q \equiv F$.For the biconditional $p \wedge q \leftrightarrow r$ to be true,$r$ must have the same truth value as $p \wedge q$.Therefore,$r \equiv F$.Now,let us evaluate the options:$(A)$ $p \vee r \equiv p \vee F \equiv p$,which is not a tautology.$(B)$ $(p \wedge r)$ $\rightarrow (p \vee r) \equiv (p \wedge F)$ $\rightarrow (p \vee F) \equiv F$ $\rightarrow p$. Since $F \rightarrow p$ is always true for any truth value of $p$,this is a tautology.$(C)$ $(p \vee r)$ $\rightarrow (p \wedge r) \equiv (p \vee F)$ $\rightarrow (p \wedge F) \equiv p$ $\rightarrow F$,which is not a tautology.$(D)$ $p \wedge r \equiv p \wedge F \equiv F$,which is a contradiction.

If $q$ is false and $p \wedge q \leftrightarrow r$ is true,then which of the following is a tautology?

Similar Questions

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

Let $p, q, r$ be three logical statements. Consider the compound statements $S_{1}: ((\sim p) \vee q) \vee ((\sim p) \vee r)$ and $S_{2}: p \rightarrow (q \vee r)$. Then,which of the following is $NOT$ true?

The statement pattern $\sim(p \vee q) \vee(\sim p \wedge q)$ is equivalent to

Which of the following sentences are statements? Give reasons for your answer.
There are $35$ days in a month.

Given the following two statements:
$(S_{1}): (q \vee p) \rightarrow (p \leftrightarrow \sim q)$ is a tautology.
$(S_{2}): \sim q \wedge (\sim p \leftrightarrow q)$ is a fallacy.
Then:

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