Mathematical reasoning practice · Mixed difficulty

The negation of ' $x \in \mathrm{R}$ if and only if $|x| \geq 0$ ' is ...... .

Negation of " 3 is an odd number and 7 is a rational number is -

The negation of the Boolean expression $\sim s \vee ( \sim r \wedge s)$ is equivalent to

The Negation of the statement $(p \wedge q) \rightarrow r$ is -

Consider the following statements :

$P$ : Suman is brilliant

$Q:$ Suman is rich

$R$ : Suman is honest

The negation of the "Suman is brilliant and dishonest if and only if Suman is rich" can be expressed as

If the truth value of the Boolean expression $\left( {\left( {p \vee q} \right) \wedge \left( {q \to r} \right) \wedge \left( { \sim r} \right) \to \left( {p \wedge q} \right)} \right)$ is false, then the truth values of statements $p$, $q$ and $r$ respectively can be

The converse of $(p \wedge(\sim q)) \Rightarrow r$ is

Among the statements :

(S1) $((p \vee q) \Rightarrow r) \Leftrightarrow(p \Rightarrow r)$

(S2) $((p \vee q) \Rightarrow r) \Leftrightarrow((p \Rightarrow r) \vee(q \Rightarrow r))$

The statement $p \rightarrow(q \rightarrow p)$ is equivalent to

A relation $R$ on the set of non-zero complex numbers is defined by ${z_1}R{z_2} \Leftrightarrow \frac{{{z_1} - {z_2}}}{{{z_1} + {z_2}}}$ is real, then $R$ is

Given that water freezes below zero degree Celsius. Consider the following statements :
$p:$ Water froze this morning, $q$: This morning temperature was below ${0^0}\mathrm{C}$
Which of the following is the correct?

The region represented by the inequality $|2 Z-3 i|<|3 Z-2 i|$ is

1) the unit disc with its centre at $Z=0$

2) the exterior of the unit circle with its centre at $Z=0$

3) the interior of a square of side 2 units with its centre at $Z=0$

4) the exterior of a square of side 2 units with its centre at $Z=0$

If $p,q,r$ have truth values $T,F,T$ respectively, which of the following is true?

If $p, q, r, s$ and $t$ are simple statements, such that $p:$ A number is terminating.
$q:$ A number is recurring.
$r$ : A number is a rational number.
$s$ : A number is an irrational number.
$t$ : A number is a real number.
Then, the compound statement, 'A number is an irrational number if and only if it is neither non-terminating nor not recurring or rational if and only if it is terminating or if non-terminating, then must be recurring and if the number is real, it can be rational or irrational', is represented by

$\sim(p \vee q) \vee(\sim p \wedge q)$ is logical equivalent to

The contrapositive of the statement "If it is raining, then I will not come", is :

$(\sim p \vee q)$ is logically equal to -

If $p \Rightarrow \left( { \sim p \vee q} \right)$ is false, the truth value of $p$ and $q$ are respectively

The contra positive of $(\sim p \wedge q) \rightarrow(q \wedge \sim r)$ is

Let $p, q, r$ be the following:

$p$ : Rohit is healthy

$q$ : Rohit is wealthy

$r$ : Rohit is wise.

The statement $p \vee q \rightarrow \sim r$ means

If the compound statement $p \rightarrow(\sim p \vee q)$ is false, then the truth values of $p$ and $q$ are respectively

The contrapositive of the statement "I go to college if its not a holiday

Consider the statement “The match will be played only if the weather is good and ground is not wet”.
Select the correct negation from the following

Which one of the following statements is not a tautology?

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

If $p$ is any statement, then which of the following is a contradiction?

The conditional statement of 'You will get a sweet dish after the dinner' is

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

The logically equivalent preposition of $p \Leftrightarrow q$ is

The contrapositive of the statement
'If 7 is greater than 5 , then 8 is greater than 6 ', is