Question
Construct the truth table for each of the following statement patterns.
(ii) (~p ∨ ~q) ↔ [~(p ∧ q)]

Answer

pq~p~qp ∧ q ~ (p ∧ q)~p ∨ ~ q$\begin{array}{c}(\sim p \vee \sim q) \leftrightarrow {(\sim(p \wedge q))}\end{array}$
TTFFFTFT
TFFTTFTT
FTTFTFTT
FFTTTFTT

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

Similar questions

Construct the truth table for each of the following: $(iv) [(p ∧ q) ∨ r] ∧ [~r ∨ (p ∧ q)]$
In $\triangle A B C$ if $a=13, b=14, c=15$ then find the values of(i) $\cos A$
(ii) $\sin \frac{A}{2}$
(iii) $\cos \frac{A}{2}$
(iv) $\tan \frac{A}{2}$
(v) $A (\triangle ABC )$
(vi) $\sin A$
What is the distance from the point $(2,3,4)$ to (i) the $XY$ plane? (ii) the $X$-axis? (iii) origin (iv) point $(-2,7,3)$.
Write the negations of the following.
i) Price increases
ii) 0! ≠ 1
iii) 5 + 4 = 9
Prove the following
(i) $2 \tan ^{-1}\left(-\frac{1}{3}\right)+\cos ^{-1}\left(\frac{3}{5}\right)=\frac{\pi}{2}$
(ii) $2 \tan ^{-1}\left(\frac{1}{3}\right)+\tan ^{-1}\left(\frac{1}{7}\right)=\frac{\pi}{4}$
Find the magnitude of following vectors:
(i) $\bar{a}=\hat{i}-2 \hat{j}+4 \hat{k}$
(ii) $\bar{b}=4 \hat{i}-3 \hat{j}-7 \hat{k}$
(iii) a vector with initial point : $(1,-3,4)$; terminal point : $(1,0,-1)$.
Construct switching circuits of the following.
i) $\quad[(p \vee(\sim p \wedge q)] \vee[(\sim q \wedge r ) \vee \sim p]$
ii) $(p \wedge q \wedge r ) \vee[p \vee(q \wedge \sim r)]$
iii) $\quad[(p \wedge r) \vee(\sim q \wedge \sim r)] \vee(\sim p \wedge \sim r)$
Find the values of the following(i) $\sin ^{-1}\left(\sin \frac{5 \pi}{3}\right)$
(ii) $\tan ^{-1}\left(\tan \frac{\pi}{4}\right)$
(iii) $\sin \left(\cos ^{-1}\left(-\frac{1}{\sqrt{2}}\right)\right)$
(iv) $\sin \left(\cos ^{-1} \frac{4}{5}+\tan ^{-1} \frac{5}{12}\right)$
Write the negations of the following statements.
i) All natural numbers are rational.
ii) Some students of class $X$ are sixteen year old.
iii) $\exists n \in N$ such that $n+8>11$
iv) $\forall x \in N , 2 x+1$ is odd
Find a unit vector (i) in the direction of $\bar{u}$ and (ii) in the direction opposite of $\bar{u}$. where $\bar{u}=8 \hat{i}+3 \hat{j}-\hat{k}$