Using truth table verify that : (p q) q p q - Vidyadip

Question

Using truth table verify that : $(p \wedge q) \vee \sim q \equiv p \vee \sim q$

✓

Answer

To verify $(p \wedge q) \vee \sim q \equiv p \vee \sim q$

$p$	$q$	$\sim q$	$(p \wedge q)$	$(p \wedge q) \vee \sim q$	$p \vee \sim q$
1	2	3	4	5	6
T	T	F	T	T	T
T	F	T	F	T	T
F	T	F	F	F	F
F	F	T	F	T	T

From columns 5 and 6 :
$(p \wedge q) \vee \sim q \equiv p \vee \sim q$

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 "Solve the Following Question.(2 Marks)" 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 $f: C \rightarrow C$ is defined by $f(x)=x^2$, write $f^{-1}(-4)$. Here, $C$ denotes the set of all complex numbers.

Write the value of $\hat{\text{i}}\times\big(\hat{\text{j}}\times\hat{\text{k}}\big).$

Construct the truth table for each of the following statement patterns: p → [~(q ∧ r)]

Let $\text{f}:\text{R}-\Big\{-\frac{3}{5}\Big\}\rightarrow\ \text{R}$ be a function defined as $\text{f(x)}=\frac{2\text{x}}{5\text{x}+3}.$ Write $f^{-1}$: Range of $\text{f}\rightarrow\ \text{R}-\Big\{-\frac{3}{5}\Big\}.$

A bag contains $4$ white balls and $2$ black balls. Another contains $3$ white balls and $5$ black balls. If one ball is drawn from each bag, find the probability that,
One is while and one is black.

Construct a $2 \times 2$ matrix $A = [a_{ij}]$ whose elements $a_{ij}$ are given by:
$\text{a}_\text{ij}=\text{e}^{2\text{ix}}\sin(\text{xj})$

Find the vector equation of line passing through the point having position vector

$5 \hat{i}+4 \hat{j}+3 \hat{k}$ and having direction ratios $-3,4,2$.

Evaluate : $\int \frac{1}{\sqrt{3 x^2-7}} \cdot d x$

If the tangent line at a point (x, y) on the curve y = f(x) is parallel to y-axis, find the value of $\frac{\text{dy}}{\text{dx}}.$

Let $R_0$ denote the set of all non-zero real numbers and let $A=R_0 \times R_0$.
If ' $k$ ' is a binary operation on adefined by, $(a, b)^*(c, d)=(a c, b d)$ for all $(a, b),(c, d) \in A$
Find the identity element in A