Mathematical Reasoning · Mathematics · MHT CET

Truth values of $\mathrm{p} \rightarrow \mathrm{r}$ is F and $\mathrm{p} \leftrightarrow \mathrm{q}$ is F . Then the truth values of $(\sim p \vee q) ...

The statement $\sim(p \leftrightarrow \sim q)$ is

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

Let $S$ be a non-empty subset of $\mathbb{R}$. Consider the following statement: p : There is a rational number $x \in \mathrm{~S}$ such that $x>0$. W...

The contrapositive of the inverse of $\mathrm{p} \rightarrow(\mathrm{p} \rightarrow \mathrm{q})$ is

If p : The total prime numbers between 2 to 100 are 26. q : Zero is a complex number. $r$ : Least common multiple (L.C.M.) of 6 and 7 is 6 . Then whic...

Contrapositive of the statement. 'If two numbers are equal, then their squares are equal' is

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

Contrapositive of the statement 'If two numbers are not equal, then their squares are not equal', is

The following statement $(\mathrm{p} \rightarrow \mathrm{q}) \rightarrow((\sim \mathrm{p} \rightarrow \mathrm{q}) \rightarrow \mathrm{q})$ is

Let $\mathrm{p}, \mathrm{q}$ and r be the statements $\mathrm{p}: \mathrm{X}$ is an equilateral triangle $\mathrm{q}: \mathrm{X}$ is isosceles triangl...

Let p : A man is judge. $\mathrm{q}: \mathrm{He}$ is honest. The inverse of $p \rightarrow q$ is

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

The converse of "If 3 is a prime number, then 3 is odd." is

If $(p \wedge \sim r) \rightarrow(\sim p \vee q)$ has truth value False, then truth values of $p, q, r$ are respectively.

Negation of the statement "The payment will be made if and only if the work is finished in time." is

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

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

Negation of the statement ' Horses have wings if and only if crows have tails. ' is

Consider the statements given by following : (A) If $3+3=7$, then $4+3=8$. (B) If $5+3=8$, then earth is flat. (C) If both (A) and (B) are true, t...

In a class of 300 students, every student reads 5 news papers and every news paper is read by 60 students. Then the number of newspapers is

Let $p, q, r$ be three statements such that the truth value of $(p \wedge q) \rightarrow(\sim q \vee r)$ is $F$. Then the truth values of $p, q, r$ ar...

The converse of $[p \wedge(\sim q)] \rightarrow r$ is

If the statements $p, q$ and $r$ have the truth values $\mathrm{F}, \mathrm{T}, \mathrm{F}$ respectively, then the truth values of the statement patte...

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

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

The new switching circuit for the following circuit by simplifying the given circuit is ...

$$\sim[(\mathrm{p} \vee \sim \mathrm{q}) \rightarrow(\mathrm{p} \wedge \sim \mathrm{q})] \equiv$$

If p and q are statements, then _________ is a contingency.

Consider the following statements p : the switch $\mathrm{S}_1$ is closed. q : the switch $\mathrm{S}_2$ is closed. $r$ : the switch $\mathrm{S}_3$ is...

The negation of contrapositive of the statement $\mathrm{p} \rightarrow(\sim \mathrm{q} \wedge \mathrm{r})$ is

Which one of the following is the pair of equivalent circuits? ...

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

If statement I : If the work is not finished on time, the contractor is in trouble. statement II : Either the work is finished on time or the contract...

If the statement $$\mathrm{p} \leftrightarrow(\mathrm{q} \rightarrow \mathrm{p})$$ is false, then true statement/statement pattern is

The statement $$[\mathrm{p} \wedge(\mathrm{q} \vee \mathrm{r})] \vee[\sim \mathrm{r} \wedge \sim \mathrm{q} \wedge \mathrm{p}]$$ is equivalent to...

The negation of the statement "The number is an odd number if and only if it is divisible by 3."

The statement $$[(p \rightarrow q) \wedge \sim q] \rightarrow r$$ is tautology, when $$r$$ is equivalent to

If $$q$$ is false and $$p \wedge q \leftrightarrow r$$ is true, then ............ is a tautology.

Negation of contrapositive of statement pattern $$(p \vee \sim q) \rightarrow(p \wedge \sim q)$$ is

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

Negation of inverse of the following statement pattern $$(p \wedge q) \rightarrow(p \vee \sim q)$$ is

Let Statement 1 : If a quadrilateral is a square, then all of its sides are equal. Statement 2: All the sides of a quadrilateral are equal, then it is...

The given following circuit is equivalent to ...

The inverse of the statement "If the surface area increase, then the pressure decreases.", is

The contrapositive of "If $$x$$ and $$y$$ are integers such that $$x y$$ is odd, then both $$x$$ and $$y$$ are odd" is

The logical statement $$(\sim(\sim \mathrm{p} \vee \mathrm{q}) \vee(\mathrm{p} \wedge \mathrm{r})) \wedge(\sim \mathrm{q} \wedge \mathrm{r})$$ is equi...

If truth value of logical statement $$(p \leftrightarrow \sim q) \rightarrow(\sim p \wedge q)$$ is false, then the truth values of $$p$$ and $$q$$ are...

The statement pattern $$\mathrm{p} \rightarrow \sim(\mathrm{p} \wedge \sim \mathrm{q})$$ is equivalent to

If $$\mathrm{p}$$ and $$\mathrm{q}$$ are true statements and $$\mathrm{r}$$ and $$\mathrm{s}$$ are false statements, then the truth values of the stat...

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

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

The given circuit is equivalent to ...

Negation of the statement "The payment will be made if and only if the work is finished in time." Is

Let $$\mathrm{p}, \mathrm{q}, \mathrm{r}$$ be three statements, then $$[p \rightarrow(q \rightarrow r)] \leftrightarrow[(p \wedge q) \rightarrow r]$$ ...

If truth values of statements $$\mathrm{p}, \mathrm{q}$$ are true, and $$\mathrm{r}$$, $$s$$ are false, then the truth values of the following stateme...

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

If $$p: \forall n \in I N, n^2+n$$ is an even number $$q: \forall n \in I N, n^2-n$$ is an odd numer, then the truth values of $$p \wedge q, p \vee q$...

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

The negation of the statement, "The payment will be made if and only if the work is finished in time" is

The negation of '$$\forall x \in N, x^2+x$$ is even number' is

If $$\mathrm{p}$$ : It is raining. $$\mathrm{q}$$ : Weather is pleasant then simplified form of the statement "It is not true, if it is raining then w...

The negation of $$p \wedge(q \rightarrow r)$$ is

If $$\mathrm{p}$$ : It is raining and $$\mathrm{q}$$ : It is pleasant, then the symbolic form of "It is neither raining nor pleasant" is

"If two triangles are congruent, then their areas are equal." is the given statement, then the contrapositive of the inverse of the given statement is...

The negation of inverse of $$\sim \mathrm{p} \rightarrow \mathrm{q}$$ is

S1 : If $$-$$7 is an integer, then $$\sqrt{-7}$$ is a complex number $$\mathrm{S} 2$$ : $$-$$7 is not an integer or $$\sqrt{-7}$$ is a complex number...

Negation of the statement : $$3+6>8$$ and $$2+3

Given $$\mathrm{p}$$ : A man is a judge, $$\mathrm{q}$$ : A man is honest If $$\mathrm{S} 1$$ : If a man is a judge, then he is honest S2 : If a man i...

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

Let $$a: \sim(p \wedge \sim r) \vee(\sim q \vee s)$$ and $$b:(p \vee s) \leftrightarrow(q \wedge r)$$. If the truth values of $$p$$ and $$q$$ are true...

If statements $$\mathrm{p}$$ and $$\mathrm{q}$$ are true and $$\mathrm{r}$$ and $$\mathrm{s}$$ are false, then truth values of $$\sim(\mathrm{p} \righ...

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

The logical statement (p $$\to$$ q) $$\wedge$$ (q $$\to$$ ~p) is equivalent to

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

Negation of the statement $$\forall x \in R, x^2+1=0$$ is

If $$p, q$$ are true statements and $$r$$ is false statement, then which of the following is correct.

p : It rains today q : I am going to school r : I will meet my friend s : I will go to watch a movie. Then symbolic form of the statement "If it does ...

Negation of $$(p \wedge q) \rightarrow(\sim p \vee r)$$ is

The negation of a statement 'x $$\in$$ A $$\cap$$ B $$\to$$ (x $$\in$$ A and x $$\in$$ B)' is

The logical expression $$\mathrm{p} \wedge(\sim \mathrm{p} \vee \sim \mathrm{q}) \equiv$$

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

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

The negation of the statement ' He is poor but happy' is

If $$p, q$$ are true statement and $$r$$ is false statement, then which of the following statements is a true statement.

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

The symbolic form of the following circuit is (where $$p, q$$ represents switches $$S_1$$ and $$s_2$$ closed respectively) ...

Let $a: \sim(p \wedge \sim r) \vee(\sim q \vee s)$ and $b:(p \vee s) \leftrightarrow(q \wedge r)$. If the truth values of $p$ and $q$ are true and tha...

5. "If two triangles are congruent, then their areas are equal" is the given statement then the contrapositive of, the inverse of the given statement ...

Which of the following statement pattern is a tautology?

If $p$ and $q$ are true and $r$ and $s$ are false statements, then which of the following is true?

The negation of " $\forall, n \in N, n+7>6$ " is .............

Which of the following statements is contingency?

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

Which of the following is not equivalent to $p \rightarrow q$.

The equivalent form of the statement $\sim(p \rightarrow \sim q)$ is $\ldots$