The logical statement (p lor q) land [(sim p | vedclass

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

Question

(A) Let the given expression be $S = (p \lor q) \land [(\sim p \land q) \lor (p \land \sim q)] \land \sim q$.Using the associative property, we can wr

Vedclass · Accepted Answer

$p \land \sim q$

Vedclass · Answer

(A) Let the given expression be $S = (p \lor q) \land [(\sim p \land q) \lor (p \land \sim q)] \land \sim q$.Using the associative property, we can write $S = (p \lor q) \land \sim q \land [(\sim p \land q) \lor (p \land \sim q)]$.First, evaluate $(p \lor q) \land \sim q$. By the distributive law, this is $(p \land \sim q) \lor (q \land \sim q)$. Since $(q \land \sim q) = F$ (a contradiction), this simplifies to $(p \land \sim q) \lor F = (p \land \sim q)$.Now substitute this back into $S$: $S = (p \land \sim q) \land [(\sim p \land q) \lor (p \land \sim q)]$.Let $A = (p \land \sim q)$. Then $S = A \land [(\sim p \land q) \lor A]$.By the absorption law, $A \land (B \lor A) = A$.Therefore, $S = A = (p \land \sim q)$.

The logical statement $(p \lor q) \land [(\sim p \land q) \lor (p \land \sim q)] \land \sim q$ is logically equivalent to ...

Similar Questions

If the truth value of the logical statement $(p \leftrightarrow \sim q) \rightarrow (\sim p \wedge q)$ is false,then the truth values of $p$ and $q$ are respectively:

In a switching circuit, if the combination $(S_1 \land S_2)$ is connected in parallel to the combination $(S'_1 \land S'_2)$, then the room is lit only when ...

The statement $(p \wedge \sim q) \wedge (\sim p \vee q)$ is a...

Which of the following statements is a tautology?

$p :$ Suman is brilliant.
$q :$ Suman is rich.
$r :$ Suman is honest.
How can the negation of the statement "Suman is rich if and only if Suman is brilliant and dishonest" be represented?

Vedclass Test Series

Exam Paper Generator

Online Exam Module