Mathematical reasoning practice · Easy

The Boolean expression $\sim \left( {p \Rightarrow \left( { \sim q} \right)} \right)$ is equivalent to

The negation of the statement ' 72 is divisible by 2 and 3 ' is

Consider the following two statements.

Statement $p$ :

The value of $\sin 120^{\circ}$ can be divided by taking $\theta=240^{\circ}$ in the equation $2 \sin \frac{\theta}{2}=\sqrt{1+\sin \theta}-\sqrt{1-\sin \theta}$.

Statement $q:$

The angles $A, B, C$ and $D$ of any quadrilateral $A B C D$ satisfy the equation $\cos \left(\frac{1}{2}(A+C)\right)+\cos \left(\frac{1}{2}(B+D)\right)=0$
Then the truth values of $p$ and $q$ are respectively.

Let $p, q, r$ be three statements such that the truth value of $\sim(\sim p \vee \sim q) \rightarrow(\sim q \vee r)$ is $F$. Then the truth values of $p, q, r$ are respectively:

Negation of the Boolean statement $(p \vee q) \Rightarrow((\sim r) \vee p)$ is equivalent to

The contrapositive of the statement "I go to school if it does not rain" is

Consider the following statements :

P : Suman is brilliant

Q: Suman is rich.

$\mathrm{R}$ : Suman is honest

the negation of the statement

"Suman is brilliant and dishonest if and only if suman is rich" can be equivalently expressed as :

Contrapositive of the statement “If two numbers are not equal, then their squares are not equal” is

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

$\,\,\,-[p \wedge(q \Rightarrow \sim r)]=\ldots \ldots$

For any two statements $p$ and $q$, $\sim \left( {p \vee q} \right) \vee \left( { \sim p \wedge q} \right)$ is logically equivalent to

If p: Nidhi is intelligent; $\mathrm{q}$ : Nidhi will pass, then the statement Nidhi is intelligent but will not pass is written in symbols as

The statement $p \wedge \sim q \rightarrow r$ is logically equivalent to

Which of the following Boolean expression is a tautology?

The statement $p \Leftrightarrow q$ is equal to -

the contrapositive of "If two triangles are identical, then these are similar" is

The proposition $\sim(p \vee \sim q) \vee \sim(p \vee q)$ is logically equivalent to

$p \wedge \left( {q \wedge r} \right)$ is logically equivalent to

The contrapositive of $p \rightarrow(\sim q \rightarrow \sim r)$ is

Which of the following statement has the truth value 'F'?

The negation of the Boolean expression $x \leftrightarrow \, \sim y$ is equivalent to