The negation of (p wedge (sim q)) vee (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 $S = (p \wedge (\sim q)) \vee (\sim p)$.Using the distributive law,we have:$S = (p \vee (\sim p)) \wedge ((\sim q) \ve

Vedclass · Accepted Answer

$p \wedge q$

Vedclass · Answer

(A) Let the given expression be $S = (p \wedge (\sim q)) \vee (\sim p)$.Using the distributive law,we have:$S = (p \vee (\sim p)) \wedge ((\sim q) \vee (\sim p))$Since $(p \vee (\sim p))$ is a tautology $(T)$,we get:$S = T \wedge ((\sim q) \vee (\sim p)) = (\sim q) \vee (\sim p)$Now,we need to find the negation of $S$:$\sim S = \sim ((\sim q) \vee (\sim p))$Using De Morgan's law,$\sim (A \vee B) = (\sim A) \wedge (\sim B)$:$\sim S = (\sim (\sim q)) \wedge (\sim (\sim p))$$\sim S = q \wedge p = p \wedge q$Thus,the negation is equivalent to $p \wedge q$.

The negation of $(p \wedge (\sim q)) \vee (\sim p)$ is equivalent to:

Similar Questions

The statement $p$ $\rightarrow (q$ $\rightarrow p)$ is equivalent to which of the following?

The negation of the statement "If $5 < 7$ and $7 > 2$,then $5 > 2$" is

Which of the following statements are true and which are false? In each case give a valid reason for saying so.
$s:$ If $x$ and $y$ are integers such that $x > y,$ then $-x < -y.$

Give three examples of sentences which are not statements. Give reasons for the answers.

For each of the following statements,determine whether an inclusive "Or" or exclusive "Or" is used. Give reasons for your answer.
The school is closed if it is a holiday or a Sunday.

Vedclass Test Series

Exam Paper Generator

Online Exam Module