Question
Construct the truth table for each of the following statement patterns.
i) $\quad p \rightarrow(q \rightarrow p)$
ii) $(\sim p \vee q) \leftrightarrow \sim(p \wedge q)$
iii) $\sim(\sim p \wedge \sim q) \vee q$
iv) $[(p \wedge q) \vee r ] \wedge[\sim r \vee(p \wedge q)]$
v) $[(\sim p \vee q) \wedge(q \rightarrow r )] \rightarrow(p \rightarrow r )$

Answer

Get the step-by-step solution for this question inside the Vidyadip app.

Get the answer in the app

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

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) $\sin \left(\cos ^{-1} \frac{4}{5}+\tan ^{-1} \frac{5}{12}\right)$
Construct the truth table for each of the following:
(iii) ~(~p ∧ ~q) ∨ q
Find the separate equations of lines represented by :
i) $x^2-4 y^2=0$
ii) $3 x^2-7 x y+4 y^2=0$
iii) $x^2+2 x y-y^2=0$
iv) $5 x^2-3 y^2=0$
Using truth tables, prove the following logical equivalences
i) $(p \wedge q) \equiv \sim(p \rightarrow \sim q)$
ii) $(p \leftrightarrow q) \equiv(p \wedge q) \vee(\sim p \wedge \sim q)$
iii) $(p \wedge q) \rightarrow r \equiv p \rightarrow(q \rightarrow r )$
iv) $p \rightarrow(q \vee r) \equiv(p \rightarrow$ q $) \vee(p \rightarrow r )$
Find the value of a for which the vectors $3 \hat{i}+2 \hat{j}+9 \hat{k}$ and $\hat{i}+a \hat{j}+3 \hat{k}$ are (i) perpendicular (ii) parallel
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 a unit vector (i) in the direction of $\bar{u}$ and (ii) in the direction opposite of $\bar{u}$. where $\bar{u}=8 \hat{i}+3 \hat{j}-\hat{k}$
The non-zero vectors $\bar{a}$ and $\bar{b}$ are not collinear find the value of $\lambda$ and $\mu$ :
(i) $\bar{a}+3 \bar{b}=2 \lambda \bar{a}-\mu \bar{b}$
(ii) $(1+\lambda) \bar{a}+2 \lambda \bar{b}=\mu \bar{a}+4 \mu \bar{b}$
(iii) $(3 \lambda+5) \bar{a}+\bar{b}=2 \mu \bar{a}+(\lambda-3) \bar{b}$
Find the acute angle between lines represented by:
i) $x^2+x y=0$
ii) $x^2-4 x y+y^2=0$
iii) $3 x^2+2 x y-y^2=0$
iv) $2 x^2-6 x y+y^2=0$
v) $x y+y^2=0$
$A (2,3), B (-1,5), C (-1,1)$ and $D (-7,5)$ are four points in the Cartesian plane.(i) Find $\overline{ AB }$ and $\overline{ CD }$.
(ii) Check if, $\overline{ CD }$ is parallel to $\overline{ AB }$.
(iii) $E$ is the point $(k, 1)$ and $\overrightarrow{ AC }$ is parallel to $\overrightarrow{ BE }$. Find $k$.