Mathematical reasoning practice · Easy

Consider the following statements:
A : Rishi is a judge.
B : Rishi is honest.
C : Rishi is not arrogant.
The negation of the statement “if Rishi is a judge and he is not arrogant, then he is honest” is

If $p:$ Ashok works hard

$q$ : Ashok gets good grade

The verbal form for $(\sim p \rightarrow q)$ is

If $p, q, r$ are substatements with truth values. $T, T, F$ then the Statement $r \rightarrow(p \wedge \sim q) \vee(\sim q \wedge \sim r)$ will be

If $p$ and $q$ are two statements. Then negation of compound statement $(\sim p \vee q)$ is

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

The negative of the proposition : “If a number is divisible by 15, then it is divisible by 5 or 3”

Converse of the statement:

If a number $n$ is even, then $n^2$ is even, is

The proposition $p \to \sim \left( {p \wedge \sim q} \right)$ is

$\sim \left( { \sim p} \right) \leftrightarrow p$ is

If $p$ and $q$ are two simple propositions, then $p \leftrightarrow \, \sim q$ is true when

Let $p$ and $q$ be the statements:

$p$ : Rakshit gets $100 \%$ marks in mathematics

$q:$ Rakshit is a good dancer.

The verbal form of $\sim p \rightarrow q$ is

For integers $m$ and $n$, both greater than 1 , consider the following three statements : < br>
$P: m$ divides $n$

$Q: m$ divides $n^2$

$R: m$ is prime,

then

Let the operations $*, \odot \in\{\wedge, \vee\}$. If $(p * q) \odot(p \odot \sim q)$ is a tautology, then the ordered pair $(*, \odot)$ is

Negation of $p \rightarrow q$ is

Let $p$ and $q$ be two propositions. Then the inverse of the implication $p \to q$ is

Negation of the statement :
$\sqrt 5$ is an integer or 5 is an irrational is

The dual of the statement $\left[ {p \vee \left( { \sim q} \right)} \right] \wedge \left( { \sim p} \right)$ is

The contrapositive statement of 'If $x^2=25$, then ( $x=5$ or $\left.x=-5\right)$ ' is ...... .

The statement $\sim[p \vee(\sim(p \wedge q))]$ is equivalent to

Which one of the following Boolean expressions is a tautology?

The contrapositive of $(p \vee q) \Rightarrow r$ is

$\,\,\,-[p \Rightarrow(\sim p \vee q)]=\ldots .$.

The inverse of the proposition $\left( {p \wedge \sim q} \right) \to r$ is

Which of the following is a statement?

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

Consider the following statements.

I. "Every rectangle is a square" is a statement.

II. "Close the door" is not a statement.

Choose the correct option.

If $p:$ Ram is smart
$q:$ Ram is intelligent
Then, the symbolic form Ram is smart and intelligent, is

Dual of ${\left( {x' \vee y'} \right)^\prime } = x \wedge y$ is

If $p \Rightarrow (q \vee r)$ is false, then the truth values of p, q, r are respectively

For any two statements $p$ and $q$, the negation of the expression $p \vee ( \sim p \wedge q)$ is