Mathematical reasoning practice · Easy

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

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 inverse of $(p \rightarrow \sim q)$ is

The statement $(p \to (q \to p)) \to (p \to (p \vee q))$ is

The negation of the statement $((A \wedge(B \vee C))$ $\Rightarrow(A \vee B)) \Rightarrow A$ is

Negation of $(p \Rightarrow q) \Rightarrow(q \Rightarrow p)$ is

Which of the following is the conditional statement $p \rightarrow q$ ?

Consider the following statements.

Statement-I: The negation of the statement "The number 2 is greater than 7" is "The number 2 is not greater than 7".

Statement-II: The negation of the statement "Every natural number is an integer" is "every natural number is not an integer".

Choose the correct option.

$\sim((\sim {p}) \wedge {q})$ is equal to

If $p \to \left( {q \vee r} \right)$ is false, then the truth values of $p,q,r$ are respectively

If the truth value of the statement $(P \wedge(\sim R)) \rightarrow$ $((\sim R) \wedge Q)$ is $F$, then the truth value of which of the following is $F$ ?

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

If $p, q, r$ are three statements and truth value of $p \wedge q \rightarrow r$ is $F$, then truth values of $p, q, r$ are respectively

The negation of the statement $(p \vee q) \wedge(q \vee(\sim r))$ is

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

$p$ : city $X$ is in U.P.

$q:$ city $X$ is in India

$r: p \rightarrow q$

Contrapositive of $r$ is

If $p, q$ and $r$ are three propositions, then which of the following combination of truth values of $p, q$ and $r$ makes the logical expression $\{(p \vee q) \wedge((\sim p) \vee r)\} \rightarrow((\sim q) \vee r)$ false ?

The negation of the statement "he is rich and happy" is given by

Consider the proposition : “If we control population growth, we prosper”. Negative of this proposition is

Let $p$ and $q$ be any two logical statements and $\mathrm{r}: \mathrm{p} \rightarrow(\sim p \vee q)$. If $r$ has a truth value $F$, then the truth values of $p$ and $q$ are respectively:

Contrapositive of the statement ‘If a function $f$ is differentiable at a, then it is also continuous at $a'$ is

Negation of the statement $p$ : for every real number, either $x > 1$ or $x < 1$ is