The negation of the Boolean expression x left | vedclass

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

Question

(C) The given expression is $x \leftrightarrow \sim y$.We know that $p \leftrightarrow q \equiv (p$ $\rightarrow q) \wedge (q$ $\rightarrow p)$.So,$x

Vedclass · Accepted Answer

$(x \wedge y) \vee (\sim x \wedge \sim y)$

Vedclass · Answer

(C) The given expression is $x \leftrightarrow \sim y$.We know that $p \leftrightarrow q \equiv (p$ $\rightarrow q) \wedge (q$ $\rightarrow p)$.So,$x \leftrightarrow \sim y \equiv (x$ $\rightarrow \sim y) \wedge (\sim y$ $\rightarrow x)$.Using the identity $p \rightarrow q \equiv \sim p \vee q$,we get:$x \leftrightarrow \sim y \equiv (\sim x \vee \sim y) \wedge (y \vee x)$.Now,we find the negation:$\sim(x \leftrightarrow \sim y) \equiv \sim((\sim x \vee \sim y) \wedge (x \vee y))$.By De Morgan's Law,$\sim(A \wedge B) \equiv \sim A \vee \sim B$:$\sim(x \leftrightarrow \sim y) \equiv \sim(\sim x \vee \sim y) \vee \sim(x \vee y)$.Applying De Morgan's Law again:$\sim(x \leftrightarrow \sim y) \equiv (x \wedge y) \vee (\sim x \wedge \sim y)$.

The negation of the Boolean expression $x \leftrightarrow \sim y$ is equivalent to

Similar Questions

Which of the following statements is logically equivalent to $\sim (p \leftrightarrow q)$?

Consider the following three statements:
$(A)$ If $3+2=7$ then $4+3=8$.
$(B)$ If $5+2=7$ then earth is flat.
$(C)$ If both $(A)$ and $(B)$ are true then $5+6=11$.
Which of the following statements is correct?

Consider the following statements:
$P :$ Ramu is intelligent
$Q :$ Ramu is rich
$R :$ Ramu is not honest
The negation of the statement "Ramu is intelligent and honest if and only if Ramu is not rich" can be expressed as:

If $p$ and $q$ are statements,then $\qquad$ is a contingency.

The negation of the statement "If a quadrilateral is a square,then it is a rhombus" is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module