Mathematical Reasoning · Mathematics · MHT CET

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MCQ (Single Correct Answer)

1

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?

MHT CET 2025 22nd April Morning Shift
2

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 $\sqrt{2}+\sqrt{3}=\sqrt{5}$

MHT CET 2025 22nd April Morning Shift
3

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

MHT CET 2025 21st April Evening Shift
4

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.

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5

The logical statement

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

is equivalent to

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6

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

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7

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

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8

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

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9

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?

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10

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

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11

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

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12
Which of the following are pairs of equivalent circuitsMHT CET 2025 19th April Evening Shift Mathematics - Mathematical Reasoning Question 11 English
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13
The statement pattern $[(p \rightarrow q) \wedge \sim q] \rightarrow r$ is a tautology when $r$ is equivalent to
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14

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?

MHT CET 2025 19th April Morning Shift
15

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

MHT CET 2024 16th May Evening Shift
16

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

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17

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

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18

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?

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19

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

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20

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?

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21

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

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22

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

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23

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

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24

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

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25

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

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26

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

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27

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

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28

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

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29

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

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30

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

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31

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

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32

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

MHT CET 2024 9th May Evening Shift
33

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

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34

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?

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35

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

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36

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

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37

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

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38

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

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39

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

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40

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

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41

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

MHT CET 2024 3rd May Evening Shift Mathematics - Mathematical Reasoning Question 38 English

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42

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

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43

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

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44

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

MHT CET 2024 3rd May Morning Shift
45

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

MHT CET 2024 2nd May Evening Shift
46

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

MHT CET 2024 2nd May Evening Shift Mathematics - Mathematical Reasoning Question 43 English

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47

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

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48

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

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49

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
50

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 Evening Shift
51

The negation of the statement

"The number is an odd number if and only if it is divisible by 3."

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52

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

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53

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

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54

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

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55

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

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56

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

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57

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.

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58

The given following circuit is equivalent to

MHT CET 2023 12th May Evening Shift Mathematics - Mathematical Reasoning Question 84 English

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59

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

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60

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

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61

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

MHT CET 2023 11th May Evening Shift
62

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

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63

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

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64

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

MHT CET 2023 10th May Evening Shift
65

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

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66

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
67

The given circuit is equivalent to

MHT CET 2023 10th May Morning Shift Mathematics - Mathematical Reasoning Question 94 English

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68

Negation of the statement

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

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69

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

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70

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

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

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71

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

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72

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

MHT CET 2022 11th August Evening Shift
73

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

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74

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

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75

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

MHT CET 2021 24th September Evening Shift
76

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

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77

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

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78

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 24th September Morning Shift
79

"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)

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80

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

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81

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

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82

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

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83

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

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84

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

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85

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

MHT CET 2021 22th September Evening Shift
86

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.

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87

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

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88

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

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89

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

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90

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

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91

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

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92

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

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93

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

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94

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

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95

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

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96

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

MHT CET 2020 19th October Evening Shift
97

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

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98

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

MHT CET 2020 16th October Evening Shift
99

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 Evening Shift
100

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
101

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

MHT CET 2020 16th October Morning Shift Mathematics - Mathematical Reasoning Question 68 English

MHT CET 2020 16th October Morning Shift
102

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......

MHT CET 2019 3rd May Morning Shift
103

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

MHT CET 2019 3rd May Morning Shift
104

Which of the following statement pattern is a tautology?

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105

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
106

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

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107

Which of the following statements is contingency?

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108

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
109

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

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110

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

MHT CET 2019 2nd May Morning Shift
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