p (p q) is logically equivalent to - Vidyadip

MCQ

$p \wedge(p \rightarrow q)$ is logically equivalent to

A
$p \vee q$
B
$\sim p \vee q$
✓
$p \wedge q$
D
$\mathrm{p} \vee \sim \mathrm{q}$

✓

Answer

Correct option: C.

$p \wedge q$

(C)
$\begin{array}{l}p \wedge(p \rightarrow q) \\ \equiv p \wedge(\sim p \vee q)\end{array}$
$\equiv( p \wedge \sim p ) \vee( p \wedge q ) \quad \ldots[$ Distributive law $]$
$\equiv F \vee(p \wedge q) \quad \ldots$ [Complement law]
$
\equiv p \wedge q\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 $\cot ^{-1} \frac{3}{4}+\sin ^{-1} \frac{5}{13}=\sin ^{-1}(k)$, then $k=$

$\int_0^{\pi / 4} \tan ^6 x \sec ^2 x d x=$

The direction angles of the line $x=4 z+3$, $y=2-3 z$ are $\alpha, \beta$ and $\gamma$, then $\cos \alpha+\cos \beta+\cos \gamma=$ __________ .

The equation of the line passing through the points $\text{a}_1\hat{\text{i}}+\text{a}_2\hat{\text{j}}+\text{a}_3\hat{\text{k}}$ and $\text{b}\hat{\text{i}}+\text{b}_2\hat{\text{j}}+\text{b}_3\hat{\text{k}}$ is:

If the function $\text{f}(\text{x})=\frac{-\text{x}}{2}+\sin\text{x}$ defined on $\Big[\frac{-\pi}{3},\frac{\pi}{3}\Big]$ is:

Two cards are drawn from a well shuffled deck of $52$ playing cards with replacement. The probability that both cards are queen is

If $\bar{a}, \bar{b}, \bar{c}$ are non-coplanar vectors and $\lambda$ is a real number then $\left[\lambda(\bar{a}+\bar{b}) \ \lambda^2 \bar{b} \ \lambda \bar{c}\right]=[\bar{a} \bar{b}+\bar{c} \bar{b}]$ for

A plane passes through $(1,-2,1)$ and is perpendicular to two planes $2 x-2 y+z=0$ and $x-y+2 z =4$. The distance of the plane from the point $(1,2,2)$ is

A bakerman sells 5 types of cakes. Profit due to sale of each type of cake is respectively ₹ 3 , ₹ 2.5, ₹ 2 , ₹ 1.5 and ₹ 1 . The demands for these cakes are 10%, 5%, 20%, 50% and 15% respectively. Then, the expected profit per cake is

$\int_{-1}^1 \log \left(\frac{2-x}{2+x}\right) d x=$