Question
Construct the truth table for each of the following:
(iii) ~(~p ∧ ~q) ∨ q
(iii) ~(~p ∧ ~q) ∨ q
✓
Answer
| p | q | ~p | ~q | ~ p ∧ ~ q | ~ (~ p ∧ ~ q) | ~ (~ p ∧ ~ q) ∧ q |
| T | T | F | F | F | T | T |
| T | F | F | T | F | T | T |
| F | T | T | F | F | T | T |
| F | F | T | T | T | T | T |
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Similar questions
Construct the truth table for each of the following: $(iv) [(p ∧ q) ∨ r] ∧ [~r ∨ (p ∧ q)]$
→If $A=\{1,2,3,4,5,6,7\}$, determine the truth value of the following.
i) $\exists x \in A$ such that $x-4=3$
ii) $\forall x \in A , \quad x+1 \geq 3$
iii) $\forall x \in A , 8-x \leq 7$
iv) $\exists x \in A$, such that $x+8=16$
→i) $\exists x \in A$ such that $x-4=3$
ii) $\forall x \in A , \quad x+1 \geq 3$
iii) $\forall x \in A , 8-x \leq 7$
iv) $\exists x \in A$, such that $x+8=16$
In the diagram $\overline{ KL }=\bar{a}, \overline{ LN }=\bar{b}, \overline{ NM }=\bar{c}$ and $\overline{ KT }=\bar{d}$. Find in terms of $\bar{a}, \bar{b}, \bar{c}$ and $\bar{d}$.(i)
(ii) $\overrightarrow{ KM }$
(iii) $\overline{ TN }$
(iv) $\overline{ MT }$
→(ii) $\overrightarrow{ KM }$
(iii) $\overline{ TN }$
(iv) $\overline{ MT }$
Prove the following
(i) $2 \tan ^{-1}\left(-\frac{1}{3}\right)+\cos ^{-1}\left(\frac{3}{5}\right)=\frac{\pi}{2}$
(ii) $2 \tan ^{-1}\left(\frac{1}{3}\right)+\tan ^{-1}\left(\frac{1}{7}\right)=\frac{\pi}{4}$
→(i) $2 \tan ^{-1}\left(-\frac{1}{3}\right)+\cos ^{-1}\left(\frac{3}{5}\right)=\frac{\pi}{2}$
(ii) $2 \tan ^{-1}\left(\frac{1}{3}\right)+\tan ^{-1}\left(\frac{1}{7}\right)=\frac{\pi}{4}$
Write the truth values of the following statements.
i) 3 is a prime number and 4 is a rational number.
ii) All flowers are red or all cows are black.
iii) If Mumbai is in Maharashtra then Delhi is the capital of India.
iv) Milk is white if and only if the Sun rises in the West.
i) 3 is a prime number and 4 is a rational number.
ii) All flowers are red or all cows are black.
iii) If Mumbai is in Maharashtra then Delhi is the capital of India.
iv) Milk is white if and only if the Sun rises in the West.
Construct the truth table for each of the following statement patterns.
(ii) (~p ∨ ~q) ↔ [~(p ∧ q)]
(ii) (~p ∨ ~q) ↔ [~(p ∧ q)]
$A (2,3), B (-1,5), C (-1,1)$ 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 $k$.
→(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 $k$.
Find the area of the regions bounded by the following curve, the $\mathrm{X}$-axis and the given lines :
(i) $y=x^2, x=1, x=2$
(ii) $y^2=4 x, x=1, x=4, y \geq 0$
(iii) $y=\sin x, x=-\frac{\pi}{2}, x=\frac{\pi}{2}$
→(i) $y=x^2, x=1, x=2$
(ii) $y^2=4 x, x=1, x=4, y \geq 0$
(iii) $y=\sin x, x=-\frac{\pi}{2}, x=\frac{\pi}{2}$
Write the duals of each of the following:
i) $(p \wedge q) \vee r$
ii) $t \vee(p \vee q)$
iii) $p \wedge[\sim q \vee(p \wedge q) \vee \sim r]$
iv) $(p \vee q) \wedge t$
v) $(p \vee q) \vee r=p \vee(q \vee r)$
vi) $p \wedge q \wedge r$
vii) $(p \wedge t) \vee(c \wedge \sim q)$
→i) $(p \wedge q) \vee r$
ii) $t \vee(p \vee q)$
iii) $p \wedge[\sim q \vee(p \wedge q) \vee \sim r]$
iv) $(p \vee q) \wedge t$
v) $(p \vee q) \vee r=p \vee(q \vee r)$
vi) $p \wedge q \wedge r$
vii) $(p \wedge t) \vee(c \wedge \sim q)$
If $\bar{a}=3 \hat{i}+4 \hat{j}-5 \hat{k}$ and $\bar{b}=3 \hat{i}-4 \hat{j}-5 \hat{k}$
(i) find $\bar{a} \cdot \bar{b}$
(ii) the angle between $\bar{a}$ and $\bar{b}$.
(iii) the scalar projection of $\bar{a}$ in the direction of $\bar{b}$.
(iv) the vector projection of $\bar{b}$ along $\bar{a}$.
→(i) find $\bar{a} \cdot \bar{b}$
(ii) the angle between $\bar{a}$ and $\bar{b}$.
(iii) the scalar projection of $\bar{a}$ in the direction of $\bar{b}$.
(iv) the vector projection of $\bar{b}$ along $\bar{a}$.