Consider the statement patterns:A. (q to p) l | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Step $1$: Analyze $A$: $(q 	o p) \lor (p 	o q) \equiv (\sim q \lor p) \lor (\sim p \lor q) \equiv (\sim q \lor q) \lor (\sim p \lor p) \equiv T

Vedclass · Accepted Answer

$A$ and $B$ are tautologies, $C$ and $D$ are contradictions.

Vedclass · Answer

(B) Step $1$: Analyze $A$: $(q 	o p) \lor (p 	o q) \equiv (\sim q \lor p) \lor (\sim p \lor q) \equiv (\sim q \lor q) \lor (\sim p \lor p) \equiv T \lor T \equiv T$. Thus, $A$ is a tautology.Step $2$: Analyze $B$: By De Morgan's Law, $\sim (p \land q) \equiv \sim p \lor \sim q$. Therefore, $(\sim p \lor \sim q) \leftrightarrow (\sim p \lor \sim q)$ is always true. Thus, $B$ is a tautology.Step $3$: Analyze $C$: $[(p \lor q) \land \sim p] \land \sim q \equiv [(p \land \sim p) \lor (q \land \sim p)] \land \sim q \equiv [F \lor (q \land \sim p)] \land \sim q \equiv (q \land \sim p \land \sim q) \equiv (q \land \sim q) \land \sim p \equiv F \land \sim p \equiv F$. Thus, $C$ is a contradiction.Step $4$: Analyze $D$: $(p \land q) \land (\sim p \lor \sim q) \equiv (p \land q \land \sim p) \lor (p \land q \land \sim q) \equiv (p \land \sim p \land q) \lor (p \land q \land \sim q) \equiv (F \land q) \lor (p \land F) \equiv F \lor F \equiv F$. Thus, $D$ is a contradiction.Conclusion: $A$ and $B$ are tautologies, $C$ and $D$ are contradictions.

Consider the statement patterns:
$A$. $(q \to p) \lor (p \to q)$
$B$. $(\sim p \lor \sim q) \leftrightarrow \sim (p \land q)$
$C$. $[(p \lor q) \land \sim p] \land \sim q$
$D$. $(p \land q) \land (\sim p \lor \sim q)$
Which of the following is true?

Similar Questions

Which of the following statement patterns is a tautology?
$S_1 \equiv (\sim q \wedge p) \wedge q$
$S_2 \equiv [p \wedge (p$ $\rightarrow q)]$ $\rightarrow q$
$S_3 \equiv (p \wedge q) \wedge (\sim p \vee \sim q)$
$S_4 \equiv (p \wedge q) \rightarrow r$

The contrapositive of $(\sim p \wedge q) \rightarrow (q \wedge \sim r)$ is

Which of the following sentences are statements? Give reasons for your answer.
"Answer this question."

The statement pattern $[(p \land q) \to (\sim p \lor r)] \lor [(\sim p \lor r) \to (p \land q)]$ is

The negation of the proposition "If $2$ is prime,then $3$ is odd" is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module

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$. $(p \land q) \land (\sim p \lor \sim q)$Which of the following is true?