Mathematical Reasoning · Mathematics · MHT CET

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

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...

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

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) ...