Mathematical reasoning practice · Easy

If $\Delta \in\{\vee, \wedge\}$, then the negation of Boolean expression $(p \rightarrow p \vee q) \Delta(p \wedge q \rightarrow q)$ is

Which of the following is not a statement?

Which of the following is equivalent to the Boolean expression $p \wedge \sim q?$

The Statement that is TRUE among the following is

If I become a teacher, then I will open a school", is

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

If $p:4$ an even prime number $q:6$ is a divisor of 12 and $r:$ the HCF of 4 and 6 is 2, then which one of the following is true?

Which of the following is false?

The statement $(p \Rightarrow q) \vee(p \Rightarrow r)$ is NOT equivalent to

Let $A$, $B$, $C$ and $D$ be four non-empty sets. The contrapositive statement of
"If $A\, \subseteq \,B$ and $B\, \subseteq \,D$, then $A\, \subseteq \,C$ " is

Simplify $\left( {p \vee q} \right) \wedge \left( {p \vee \sim q} \right)$

Consider the following statements:

$P$ : I have fever

$Q$ : I will not take medicine

$R$ : I will take rest

The statement "If I have fever, then I will take medicine and I will take rest

Let $R$ be the set of real numbers and $x \in R$. Then, $x+3=8$ is

The proposition $p \to \, \sim \,(p \wedge \sim q)$ is equivalent to

Let

$p$ : Ramesh listens to music.

$q:$ Ramesh is out of his village.

$r$ : It is Sunday.

$s$ : It is Saturday.

Then the statement "Ramesh listens to music only if he is in his village and it is Sunday or Saturday" can be expressed as

If $(p \to (p \wedge \sim q)$ is false, then the truth values of p and q are respectively

Negation of statement : if we control population growth we prosper, is

The contrapositive of the statement “ If I reach the station in time, then I will catch the train” is

A compound sentence formed by two simple statements $p$ and $q$ using connective 'or' is called

Contrapositive of $p \rightarrow(q \rightarrow r)$ is logically equivalent to

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 -

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

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?

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