Let $\mathrm{A}=\left(\begin{array}{cc}2 & -1 \\ 0 & 2\end{array}\right)$. If $\mathrm{B}=1-{ }^5 \mathrm{C}_1(\operatorname{adj} \mathrm{~A})+{ }^5 \mathrm{C}_2(\operatorname{adj} \mathrm{~A})^2-\ldots \ldots-{ }^5 \mathrm{C}_5(\operatorname{adj} \mathrm{~A})^5$, then the sum of all...

Let $r \in\{p, q, \sim p, \sim q\}$ be such that the logical statement $r \vee(-p) \Rightarrow(p \wedge q) \vee r$ is a tautology. Then...

Consider the following statements :
A : Rishi is a judge.
B : Rishi is honest.
C : Rishi is not arrogant.
The negation of...

The negation of the Boolean expression $((\sim q) \wedge p) \Rightarrow((\sim p) \vee q)$ is logically equivalent to

Let $\Delta \in\{\wedge, \vee, \Rightarrow, \Leftrightarrow\}$ be such that $(p \wedge q) \Delta((p \vee q) \Rightarrow q)$ is a tautology. Then $\Delta$ is equal to...

Let p, q, r be three logical statements. Consider the compound statements

Then, which of...

The Boolean expression $\left(\sim\left(p^{\wedge} q\right)\right) \vee q$ is equivalent to :

Let $\Delta, \nabla \in\{\wedge, \vee\}$ be such that $p \nabla q \Rightarrow((p \nabla q) \nabla r)$ is a tautology. Then $(p \nabla q) \Delta r$...

The number of choices of $\Delta \in\{\wedge, \vee, \Rightarrow, \Leftrightarrow\}$, such that $(p \Delta q) \Rightarrow((p \Delta \sim q) \vee((\sim p) \Delta q))$ is a...

Consider the following two propositions:

If the proposition $p \rightarrow((\sim p) \vee q)$ is evaluated...