(p wedge sim q wedge sim r) vee (sim p wedge | vedclass

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

Question

(D) Let the given expression be $S = (p \wedge \sim q \wedge \sim r) \vee (\sim p \wedge q \wedge \sim r) \vee (\sim p \wedge \sim q \wedge r)$.This e

Vedclass · Accepted Answer

$(\sim ((p \wedge q) \vee (q \wedge r) \vee (r \wedge p)) \wedge (p \vee q \vee r))$

Vedclass · Answer

(D) Let the given expression be $S = (p \wedge \sim q \wedge \sim r) \vee (\sim p \wedge q \wedge \sim r) \vee (\sim p \wedge \sim q \wedge r)$.This expression represents the condition where exactly one of the three propositions $p, q, r$ is true.Consider the expression $(p \vee q \vee r) \wedge \sim ((p \wedge q) \vee (q \wedge r) \vee (r \wedge p))$.$(p \vee q \vee r)$ is true if at least one of $p, q, r$ is true.$((p \wedge q) \vee (q \wedge r) \vee (r \wedge p))$ is true if at least two of $p, q, r$ are true.Therefore,their conjunction is true if and only if exactly one of $p, q, r$ is true.This matches the given expression $S$.Thus,the correct option is $D$.

$(p \wedge \sim q \wedge \sim r) \vee (\sim p \wedge q \wedge \sim r) \vee (\sim p \wedge \sim q \wedge r)$ is equivalent to-

Similar Questions

The contrapositive of $\sim q \to p$ is equivalent to

For each of the following compound statements,first identify the connecting words and then break it into component statements.
$x=2$ and $x=3$ are the roots of the equation $3x^{2} - x - 10 = 0$.

The statement $(p \wedge (\sim q))$ $\Rightarrow (p$ $\Rightarrow (\sim q))$ is

$\sim (p \vee q) \vee (\sim p \wedge q)$ is logically equivalent to

If the truth value of the statement pattern $( \sim p \land q) \lor ( \sim p \land \sim q) \lor (p \land \sim q)$ is $F$, then the truth values of $(p \lor \sim q)$ and $(p \to q)$ are ... respectively.

Vedclass Test Series

Exam Paper Generator

Online Exam Module