Mathematical reasoning practice · Mixed difficulty

The contrapositive of the inverse of $(p \rightarrow \sim q)$ is

Which of the following statement is a tautology?

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

${p} \vee({p} \wedge {q})$ is equivalent to

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

Which of the following is not a proposition?

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

The Boolean expression $\sim \left( {p \Rightarrow \left( { \sim q} \right)} \right)$ is equivalent to

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

The statement $B \Rightarrow((\sim A) \vee B)$ is equivalent to

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

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

The negation of the statement ' 72 is divisible by 2 and 3 ' is

Consider the following two statements.

Statement $p$ :

The value of $\sin 120^{\circ}$ can be divided by taking $\theta=240^{\circ}$ in the equation $2 \sin \frac{\theta}{2}=\sqrt{1+\sin \theta}-\sqrt{1-\sin \theta}$.

Statement $q:$

The angles $A, B, C$ and $D$ of any quadrilateral $A B C D$ satisfy the equation $\cos \left(\frac{1}{2}(A+C)\right)+\cos \left(\frac{1}{2}(B+D)\right)=0$
Then the truth values of $p$ and $q$ are respectively.