Mathematical reasoning practice · Mixed difficulty

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

The negation of the compound proposition $p \vee \left( { \sim p \vee q} \right)$ 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 compound statement $(\sim(P \wedge Q)) \vee((\sim P) \wedge Q) \Rightarrow((\sim P) \wedge(\sim Q))$ is equivalent to

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 $(p \vee q) \wedge(p \vee \sim r)$ is

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

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