The Boolean expression sim (p q) ( p q) is equivalent to - Vidyadip

MCQ

The Boolean expression sim$\sim(p \vee q) \vee(\sim p \wedge q)$ is equivalent to

A
p
B
q
C
$\sim \mathrm{q}$
✓
$\sim \mathrm{p}$

✓

Answer

Correct option: D.

$\sim \mathrm{p}$

(D)
$\sim(p \vee q) \vee(\sim p \wedge q)$
$\equiv(\sim p \wedge \sim q) \vee(\sim p \wedge q) \ldots[$ De Morgan's law]
$\equiv \sim p \wedge(\sim q \vee q) \quad \ldots[$ Distributive law $]$
$\equiv \sim p \wedge T \quad \ldots[$ Complement law $]$
$\equiv \sim p \quad \ldots$ [Identity law]

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from Mathematical Logic→Mathematical Logic — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

If $f(x)=3 x^3-9 x^2-27 x+15,$ then the maximum value of $f(x)$ is

In $\triangle A B C, \frac{\cos A}{a}+\frac{\cos B}{b}+\frac{\cos C}{c}=$

If equation $\tan \theta+\tan 2 \theta+\tan \theta \tan 2 \theta=1, \theta=$

Which of the following is NOT equivalent to p→q.

The equation of a plane which cuts equal intercepts of unit length on the axes is

If $\vec{\text{a}}$ and $\vec{\text{b}}$ are two unit vectors inclined at an angle $\theta$, such that $\big|\vec{\text{a}}+\vec{\text{b}}\big|<1,$ then:

If the angle $\theta$ is acute, then the acute angle between $x^2(\cos \theta-\sin \theta)+2 x y \cos \theta+y^2(\cos \theta+\sin \theta)=0$ is

The distance between the planes $2x + 2y - z +2 = 0$ and $4x + 4y - 2z + 5 = 0$ is:

$\int_0^2\left[x^2\right] d x=$

The points with position vectors $20 \hat{ i }+ p \hat{ j }$, $5 \hat{i}-\hat{j}$ and $10 \hat{i}-13 \hat{j}$ are collinear. The value of $p$ is