# Mathematical Reasoning · Mathematics · MHT CET

Start Practice## MCQ (Single Correct Answer)

MHT CET 2023 14th May Evening Shift

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

MHT CET 2023 14th May Evening Shift

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

MHT CET 2023 14th May Morning Shift

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

MHT CET 2023 14th May Morning Shift

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

MHT CET 2023 13th May Evening Shift

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

MHT CET 2023 13th May Evening Shift

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

MHT CET 2023 13th May Morning Shift

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

MHT CET 2023 13th May Morning Shift

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

MHT CET 2023 12th May Evening Shift

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...

MHT CET 2023 12th May Evening Shift

The given following circuit is equivalent to
...

MHT CET 2023 12th May Morning Shift

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

MHT CET 2023 12th May Morning Shift

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

MHT CET 2023 11th May Evening Shift

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...

MHT CET 2023 11th May Evening Shift

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...

MHT CET 2023 11th May Morning Shift

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

MHT CET 2023 10th May Evening Shift

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...

MHT CET 2023 10th May Evening Shift

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

MHT CET 2023 10th May Morning Shift

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

MHT CET 2023 10th May Morning Shift

The given circuit is equivalent to
...

MHT CET 2023 9th May Evening Shift

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

MHT CET 2023 9th May Evening Shift

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

MHT CET 2023 9th May Morning Shift

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...

MHT CET 2023 9th May Morning Shift

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

MHT CET 2022 11th August Evening Shift

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$...

MHT CET 2022 11th August Evening Shift

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

MHT CET 2022 11th August Evening Shift

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

MHT CET 2021 24th September Evening Shift

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

MHT CET 2021 24th September Evening Shift

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...

MHT CET 2021 24th September Morning Shift

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

MHT CET 2021 24th September Morning Shift

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

MHT CET 2021 23rd September Evening Shift

"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...

MHT CET 2021 23rd September Evening Shift

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

MHT CET 2021 23th September Morning Shift

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...

MHT CET 2021 23th September Morning Shift

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

MHT CET 2021 22th September Evening Shift

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...

MHT CET 2021 22th September Evening Shift

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

MHT CET 2021 22th September Evening Shift

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...

MHT CET 2021 22th September Morning Shift

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...

MHT CET 2021 22th September Morning Shift

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

MHT CET 2021 21th September Evening Shift

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

MHT CET 2021 21th September Evening Shift

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

MHT CET 2021 21th September Morning Shift

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

MHT CET 2021 21th September Morning Shift

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

MHT CET 2021 20th September Evening Shift

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 ...

MHT CET 2021 20th September Evening Shift

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

MHT CET 2021 20th September Morning Shift

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

MHT CET 2021 20th September Morning Shift

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

MHT CET 2020 19th October Evening Shift

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

MHT CET 2020 19th October Evening Shift

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

MHT CET 2020 16th October Evening Shift

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

MHT CET 2020 16th October Evening Shift

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

MHT CET 2020 16th October Morning Shift

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

MHT CET 2020 16th October Morning Shift

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

MHT CET 2019 3rd May Morning Shift

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...

MHT CET 2019 3rd May Morning Shift

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 ...

MHT CET 2019 3rd May Morning Shift

Which of the following statement pattern is a tautology?

MHT CET 2019 2nd May Evening Shift

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

MHT CET 2019 2nd May Evening Shift

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

MHT CET 2019 2nd May Evening Shift

Which of the following statements is contingency?

MHT CET 2019 2nd May Morning Shift

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

MHT CET 2019 2nd May Morning Shift

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

MHT CET 2019 2nd May Morning Shift

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