Which of the following is always true? - Vidyadip

MCQ

Which of the following is always true?

A
$\sim(p \rightarrow q) \equiv \sim q \rightarrow \sim p$
B
$\sim(p \vee q) \equiv p \vee \sim q$
✓
$\sim(p \rightarrow q) \equiv p \wedge \sim q$
D
$\sim(p \vee q) \equiv \sim p \vee \sim q$

✓

Answer

Correct option: C.

$\sim(p \rightarrow q) \equiv p \wedge \sim q$

(C)
$\begin{array}{l} p \rightarrow q \equiv \sim p \vee q \\ \therefore \quad \sim(p \rightarrow q) \equiv p \wedge \sim q\end{array}$

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

The principal value branch of $\sec ^{-1} x$ is

The direction ratios of the diagonals of a cube which joins the origin to the opposite corner are (when the 3 concurrent edges of the cube are coordinate axes)

The probability distribution of a r.v. $X$ is

X	-1.5	-0.5	0.5	1.5	2.5
P($\mathrm{X}=\boldsymbol{x}$)	0.05	0.2	0.15	0.25	0.35

Then the c.d.f. of X is

If the sides of a triangle are $3,5,7$, then

Let [x] denote the greatest integer less than or equal to $x$. If $f(x) = \sin^{-1}x$, $g(x) = [x^2]$ and $\text{h(x)}=2\text{x},\frac{1}{2}\leq\text{x}\leq\frac{1}{\sqrt{2}},$ then

The solution of the differential equation $(\text{x}^{2}+1)\frac{\text{dy}}{\text{dx}}+(\text{y}^{2}+1)=0$ is:

If $\theta$ is the angle between the vectors $\overline{ a }$ and $\overline{ b }$ and $|\overline{ a } \times \overline{ b }|=\overline{ a } \cdot \overline{ b }$, then $\theta$ is equal to

$\int\frac{\text{x}}{4+\text{x}^4}\text{ dx}$ is equal to:

If $\text{f}(\text{x})=\sqrt{\text{x}^2+6\text{x}+9},$ then $f'(x)$ is equal to:

If $f(x)=\int_{-1}^x|t| d t$, then for any $x \geq 0, f (x)$ Is equal to