Mathematical Reasoning · Mathematics · MHT CET

The negation of statement pattern $(\mathrm{p} \wedge \sim \mathrm{q}) \rightarrow(\mathrm{p} \vee \sim \mathrm{q})$ is

If p : switch $\mathrm{S}_1$ is closed, q : switch $\mathrm{S}_2$ is closed then correct interpretation from the following circuit is

Which of the following statement is a tautology?

If $p, q, r, s$ are statements, where, $\mathrm{p}: \mathrm{A}^2-\mathrm{B}^2=(\mathrm{A}-\mathrm{B})(\mathrm{A}+\mathrm{B}) ; \mathrm{A}, \mathrm{B}$ are matrices, $A B \neq B A$

q: $5 \leq 5$

r: ${ }^8 \mathrm{C}_1+{ }^8 \mathrm{C}_2+{ }^8 \mathrm{C}_3+\ldots \ldots \ldots . .+{ }^8 \mathrm{C}_8=256$

s: Maximum value of ${ }^8 \mathrm{C}_{\mathrm{r}}$ is 70 then the statement from the following having truth value true is ….

If the truth value of the expression $[(p \vee q) \wedge(q \rightarrow r) \wedge(\sim r)] \rightarrow(p \wedge q)$ is False, then truth values of $p, q, r$ are respectively.

Consider statements $\mathrm{p}: \mathrm{S}_1$ is closed; $\mathrm{q}: \mathrm{S}_2$ is closed; $\mathrm{r}: \mathrm{S}_3$ is closed. The simplified equivalent circuit diagram and its logical statement for the switching circuit is respectively.

Consider the following three statements

(A) If $3+2=7$ then $4+3=8$.

(B) If $5+2=7$ then earth is flat.

(C) If both (A) and (B) are true then $5+6=11$. Which of the following statements is correct?

If $p \equiv$ The switch $S_1$ is closed, $q \equiv$ The switch $\mathrm{S}_2$ is closed, $\mathrm{r} \equiv$ switch $\mathrm{S}_3$ is closed, then symbolic form of following switching circuit is equivalent to

If the statements $p, q$ and $r$ are true, false and true statements respectively, then the truth value of the statement pattern $[\sim \mathrm{q} \wedge(\mathrm{p} \vee \sim \mathrm{q}) \wedge \sim \mathrm{r}] \vee \mathrm{p}$ and the truth value of its dual statement respectively are

The negation of the statement "The triangle is an equilateral or isosceles triangle and the triangle is not isosceles and it is right angled" is

Consider the statements given by following

(A) If $4+3=8$, then $5+3=9$

(B) If $6+4=10$, then moon is flat

(C) If both (A) and (B) are true, then $5+6=17$

Then which of the following statement is correct?

Number of switches in alternative equivalent simple circuit for the circuit is (are)

Which of the following is the negation of the statement " For all M>0, there exist $x \in \mathrm{~s}$ such that $x \geqslant \mathrm{M}^{\prime \prime}$

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

$p:$ If 7 is an odd number then 7 is divisible by 2 .

q : If 7 is prime number then 7 is an odd number. If $V_1$ and $V_2$ are respective truth values of contrapositive of p and q then $\left(\mathrm{V}_1, \mathrm{~V}_2\right) \equiv$

If $p$ : switch $S_1$ is closed, $q$ : switch $S_2$ is closed, $r$ : switch $S_3$ closed, then the symbolic form of the following switching circuit is equivalent to

Switching Circuit:

If the truth value of the statement pattern $[p \wedge \sim r] \rightarrow \sim r \wedge q$ is False, then which of the following has truth value False?

Which of the following statements has the truth value T ?

A: cube roots of unity are in Geometric progression and their sum is 1

B: $4+7>10$ iff $2+8<10$

C: $\exists x \in \mathbb{N}$ such that $x^2-3 x+2=0$ and $\exists \mathrm{n} \in \mathbb{N}$ such that n is an odd number

D: $3+\mathrm{i}$ is a complex number or $\sqrt{2}+\sqrt{3}=\sqrt{5}$

If $\{(\mathrm{p} \wedge \sim \mathrm{q}) \wedge(\mathrm{p} \wedge \mathrm{r})\} \rightarrow \sim \mathrm{p} \vee \mathrm{q}$ has truth value false then truth values of the statements $p, q, r$ are respectively

The correct simplified circuit diagram for the logical statement $[\{\mathrm{q} \wedge(\sim \mathrm{q} \vee \mathrm{r})\} \wedge\{\sim \mathrm{p} \vee(\mathrm{p} \wedge \sim \mathrm{r})\}] \vee(\mathrm{p} \wedge \mathrm{r})$ Where $p, q, r$ represents switches $s_1, s_2, s_3$ respectively.

The logical statement

$$ [\sim(\sim p \vee q) \vee(p \wedge r) \wedge(\sim q \wedge r)] $$

is equivalent to

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

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

The equivalent statement of "If three vertices of a triangle are represented by cube roots of unity, then the triangle is an equilateral triangle" is

If a statement $q$ has truth value False and $(\mathrm{p} \wedge \mathrm{q}) \leftrightarrow \mathrm{r}$ has truth value True then which of the following has truth value true?

The logically equivalent statement of $(\sim \mathrm{p} \wedge \mathrm{q}) \vee(\sim \mathrm{p} \wedge \sim \mathrm{q}) \vee(\mathrm{p} \wedge \sim \mathrm{q})$ is

The last column in the truth table of the statement pattern $[\mathrm{p} \rightarrow(\mathrm{q} \wedge \sim \mathrm{p})] \vee[(\mathrm{p} \vee \sim \mathrm{q}) \wedge \mathrm{p}]$ is

Consider the three statements

$\mathrm{p}: \forall \mathrm{n} \in \mathbb{N}, 10 \mathrm{n}-3$ is a prime number, when n is not divisible by 3.

$\mathrm{q}: \frac{2}{\sqrt{3}}, \frac{-2}{\sqrt{3}}, \frac{-1}{\sqrt{3}}$ are the direction cosines of a directed line.

$\mathrm{r}: \sin x$ is an increasing function in the interval $\left[\frac{-\pi}{2}, \frac{\pi}{2}\right]$.

Then which of the following statement pattern has truth value true?

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

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 $x>0$.

Which of the following statements is the negation of the statement p?

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 which of the following is correct?

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 triangle

r: q $\vee \sim p$,

then the equivalent statement of $r$ is

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, then $5+6=17$.

Then which of the following statements is correct?

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 $p, q, r$ are respectively

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 patterns $(p \wedge \sim q) \rightarrow r$ and $(p \vee q) \rightarrow r$ are respectively

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 closed.

Then the switching circuit represented by the statement $(p \wedge q) \vee(\sim p \wedge(\sim q \vee p \vee r))$ 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 contractor is in trouble. then

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 a square.

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 equivalent to

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 respectively

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 statement patterns $$(p \wedge q) \vee r$$ and $$(\mathrm{p} \vee \mathrm{s}) \leftrightarrow(\mathrm{q} \wedge \mathrm{r})$$ are respectively

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 $$[p \rightarrow(q \rightarrow r)] \leftrightarrow[(p \wedge q) \rightarrow r]$$ is

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

$$\begin{aligned} & \mathrm{a}: \sim(\mathrm{p} \wedge \sim \mathrm{r}) \vee(\sim \mathrm{q} \vee \mathrm{s}) \\ & \mathrm{b}:(\sim \mathrm{q} \wedge \sim \mathrm{r}) \leftrightarrow(\mathrm{p} \vee \mathrm{s}) \\ & \mathrm{c}:(\sim \mathrm{p} \vee \mathrm{q}) \rightarrow(\mathrm{r} \wedge \sim \mathrm{s}) \end{aligned}$$

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 $$p \wedge q, p \vee q$$ and $$p \rightarrow q$$ are respectively

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 weather is not pleasant" is

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

(Where $$\mathrm{p}$$ : Two triangles are congruent, $$\mathrm{q}$$ : Their areas are equal)

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 $$2+3<6$$ 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 is a judge, then he is not honest

S3 : A man is not a judge or he is honest Then

S4 : A man is a judge and he is honest

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 and that of $$r$$ and $$s$$ are false, then the truth values of $$a$$ and $$b$$ are respectively

If statements $$\mathrm{p}$$ and $$\mathrm{q}$$ are true and $$\mathrm{r}$$ and $$\mathrm{s}$$ are false, then truth values of $$\sim(\mathrm{p} \rightarrow \mathrm{q}) \leftrightarrow(\mathrm{r} \wedge \mathrm{s})$$ and $$(\sim \mathrm{p} \rightarrow \mathrm{q}) \wedge(\mathrm{r} \leftrightarrow \mathrm{s})$$ are respectively.

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 not rain today or I won't go to school, then I will meet my friend and I will go to watch a movie" is

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 that of $r$ and $s$ are false, then the truth values of $a$ and $b$ are respectively......

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 is

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 $\ldots$