$ \sim \left( { \sim p} \right) \leftrightarrow p$ is

Neither a contradiction nor a tautology

The contrapositive of the statement ${ }^\alpha$ if $2^2=5$, then I get first class" is

If I do not get a first class, then $2^2=5$

If I get a first class, then $2^2=5$

The contrapositive statement of 'If $x^2=25$, then ( $x=5$ or $\left.x=-5\right)$ ' is ...... .

If $x \neq 5$ and $x \neq-5$, then $x^2 \neq 25$

If $x^2 \neq 25$, then $x \neq 5$ and $x \neq-5$

If $x \neq 5$ or $x \neq-5$, then $x^2=25$

If $x \neq 5$ and $x \neq-5$, then $x^2=25$

Dual of ${\left( {x' \vee y'} \right)^\prime } = x \wedge y$ is

$\left( {x' \vee y'} \right) = x \vee y$

${\left( {x' \wedge y'} \right)^\prime } = x \wedge y$

Back to MATHEMATICAL REASONING

Your Progress

0 / 232 Answered

Correct

Incorrect

Accuracy

JEE • MATHEMATICS • MATHEMATICAL REASONING

Mathematical reasoning practice · Mixed difficulty

Choose an answer to check it, or open “View answer” to study the explanation. Sign in to save progress to your account.

Practice format and chapter quiz

These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

Take a chapter quiz →

Showing 91-120 of 232 questions

Preparing practice and saved progress…

91 Easy

91 of 232

Understanding +4 | -1

\sim \left( { \sim p} \right) \leftrightarrow p

View answer and explanation

Correct option: A

A tautology

Option A is correct because the double negation of p is equivalent to p, making the biconditional a tautology.

92 Easy

92 of 232

Understanding +4 | -1

p

and

q

are two simple propositions, then

p \leftrightarrow \, \sim q

is true when

View answer and explanation

Correct option: C

p

is false and

q

is true

Option C (

p

is false and

q

is true) is correct because the biconditional is true when both sides have opposite truth values, and since

q

is negated,

p

must be false and

q

must be true.

93 Easy

93 of 232

Understanding +4 | -1

Let

p

and

q

be the statements:

p

: Rakshit gets

100 \%

marks in mathematics

q:

Rakshit is a good dancer.

The verbal form of

\sim p \rightarrow q

View answer and explanation

Correct option: A

If Rakshit does not get

100 \%

marks in mathematics, then Rakshit is a good dancer

Option A is correct because it accurately represents the conditional statement

\sim p \rightarrow q

in verbal form.

94 Easy

94 of 232

Analyzing +4 | -1

For integers

m

and

n

, both greater than 1 , consider the following three statements : < br>

P: m

divides

n

Q: m

divides

n^2

R: m

is prime,

then

View answer and explanation

Correct option: A

Q \wedge R \rightarrow P

Option A (

Q \wedge R \rightarrow P

) is correct because if

m

divides

n^2

and

m

is prime, then

m

must divide

n

95 Medium

95 of 232

Analyzing +4 | -1

The conditional statement

\left( {\left( {p \wedge q} \right) \to \left( {\left( { \sim p} \right) \vee r} \right)} \right) \vee \left( {\left( {\left( { \sim p} \right) \vee r} \right) \to \left( {p \wedge q} \right)} \right)

is:

View answer and explanation

Correct option: A

A tautology

Option A (A tautology) is correct because the given statement is of the form (A -> B) v (B -> A), which is always true regardless of the truth values of A and B.

96 Medium

96 of 232

Understanding +4 | -1

Negation of the statement

(p \wedge r) \longrightarrow(r \vee q)

View answer and explanation

Correct option: B

(p \wedge r) \wedge(\sim r \wedge \sim q)

Option B (

(p \wedge r) \wedge(\sim r \wedge \sim q)

) is correct because the negation of

p \rightarrow q

p \wedge \sim q

97 Easy

97 of 232

Analyzing +4 | -1

Let the operations

*, \odot \in\{\wedge, \vee\}

. If

(p * q) \odot(p \odot \sim q)

is a tautology, then the ordered pair

(*, \odot)

View answer and explanation

Correct option: B

(\vee, \vee)

Option B ((\vee, \vee)) is correct because it results in a tautology when substituted into the given expression.

98 Medium

98 of 232

Analyzing +4 | -1

The following statement

(p \rightarrow q) \rightarrow[(\sim p \rightarrow q) \rightarrow q]

View answer and explanation

Correct option: D

A tautology

Option D (A tautology) is correct because the given statement simplifies to

(p \rightarrow q) \rightarrow (p \rightarrow q)

, which is always true regardless of the truth values of p and q.

99 Medium

99 of 232

Understanding +4 | -1

If a positive integer

\mathrm{n}

is divisible by 9 , then the sum of the digits of

n

is divisible by 9 . So which statement is it contrapositive.

View answer and explanation

Correct option: B

(sum of digits of

n

is not divisible by 9 )

\Rightarrow

(

\mathrm{n}

is not divisible by 9 )

The correct answer is (sum of digits of n is not divisible by 9) => (n is not divisible by 9) because it is the contrapositive of the given statement.

100 Easy

100 of 232

Understanding +4 | -1

Negation of

p \rightarrow q

View answer and explanation

Correct option: A

p \wedge(\sim q)

Option A (

p \wedge (\sim q)

) is correct because it represents the negation of the conditional statement

p \rightarrow q

101 Easy

101 of 232

Remembering +4 | -1

Let

p

and

q

be two propositions. Then the inverse of the implication

p \to q

View answer and explanation

Correct option: B

\sim p \to \sim q

Option B (

\sim p \to \sim q

) is correct because the inverse of the implication

p \to q

is defined as

\sim p \to \sim q

102 Easy

102 of 232

Understanding +4 | -1

Negation of the statement :

\sqrt 5

is an integer or 5 is an irrational is

View answer and explanation

Correct option: D

\sqrt 5

is not an integer and 5 is not irrational

Option D (

\sqrt 5

is not an integer and 5 is not irrational) is correct because it represents the negation of the given statement using De Morgan's Law.

103 Easy

103 of 232

Understanding +4 | -1

The dual of the statement

\left[ {p \vee \left( { \sim q} \right)} \right] \wedge \left( { \sim p} \right)

View answer and explanation

Correct option: B

\left( {p \wedge \sim q} \right) \vee \sim p

Option B is correct because the dual of a statement is obtained by replacing

\wedge

with

\vee

and

\vee

with

\wedge

104 Medium

104 of 232

Understanding +4 | -1

Consider the statements
(i) Two plus three is five.
(ii) Every square is a rectangle.
(iii) Sun rises in the East.
(iv) The Earth is a star.
Which of the above statements having truth value

(\mathrm{T})

View answer and explanation

Correct option: D

All of these

The correct answer is 'All of these' because all the statements are true.

105 Medium

105 of 232

Understanding +4 | -1

The contrapositive of the statement

{ }^\alpha

2^2=5

, then I get first class" is

View answer and explanation

Correct option: B

If I do not get first class, then

2^2 \neq 5

Option B (If I do not get first class, then

2^2 \neq 5

) is correct because it is the contrapositive of the given statement, negating both the hypothesis and the conclusion and reversing the implication.

Explore Other Chapters in MATHEMATICS

View All →

SEQUENCE OF SERIES 1764 MCQs DEFINITE INTEGRATION 1443 MCQs MATRICES 1363 MCQs INDEFINITE INTEGRATION 1179 MCQs PROBABILITY 1146 MCQs COMPLEX NUMBERS 980 MCQs

106 Easy

106 of 232

Understanding +4 | -1

The contrapositive statement of 'If

x^2=25

, then (

x=5

\left.x=-5\right)

' is ...... .

View answer and explanation

Correct option: C

x \neq 5

and

x \neq-5

, then

x^2 \neq 25

Option D is correct because it correctly identifies both the contrapositive and converse statements of the given conditional statement.

107 Easy

107 of 232

Analyzing +4 | -1

The statement

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

is equivalent to

View answer and explanation

Correct option: D

\sim(p \vee q)

Option D (

\sim(p \vee q)

) is correct because by applying De Morgan's laws and simplification rules, the given statement is logically equivalent to

\sim p \wedge \sim q

, which is the same as

\sim(p \vee q)

108 Medium

108 of 232

Analyzing +4 | -1

The number of values of

r \in\{p, q, \sim p, \sim q\}

for which

((p \wedge q) \Rightarrow(r \vee q)) \wedge((p \wedge r) \Rightarrow q)

is a tautology, is

View answer and explanation

Correct option: C

The correct answer is 2 because only two values of r (

\sim p

and q) make the given expression a tautology.

109 Easy

109 of 232

Analyzing +4 | -1

Which one of the following Boolean expressions is a tautology?

View answer and explanation

Correct option: A

\left( {p \vee q} \right) \vee \left( {p \vee \sim q} \right)

Option A (

\left( {p \vee q} \right) \vee \left( {p \vee \sim q} \right)

) is correct because it simplifies to

p \vee (q \vee \sim q)

, which is always true (a tautology).

110 Easy

110 of 232

Understanding +4 | -1

The contrapositive of

(p \vee q) \Rightarrow r

View answer and explanation

Correct option: C

\sim {r} \Rightarrow-{p} \vee-{q}

Option C (A.P., G.P. and H.P.) is correct because if all numbers are equal and non-zero, they satisfy the conditions for being in arithmetic, geometric, and harmonic progressions.

111 Easy

111 of 232

Application +4 | -1

\,\,\,-[p \Rightarrow(\sim p \vee q)]=\ldots .

View answer and explanation

Correct option: D

p \wedge \sim q

Option D (

p \wedge \sim q

) is correct because by applying logical equivalences and De Morgan's law, the given expression simplifies to this form.

112 Easy

112 of 232

Understanding +4 | -1

The inverse of the proposition

\left( {p \wedge \sim q} \right) \to r

View answer and explanation

Correct option: B

\sim p \vee q \to \sim r

Option B (

\sim p \vee q \to \sim r

) is correct because it represents the inverse of the given proposition, which involves negating the antecedent and consequent.

113 Easy

113 of 232

Understanding +4 | -1

Which of the following is a statement?

View answer and explanation

Correct option: C

6 is a natural number

Option C (6 is a natural number) is the correct answer because it is a declarative sentence that is either true or false, making it a statement.

114 Easy

114 of 232

Analyzing +4 | -1

The negation of the Boolean expression

(( \sim q) \wedge p) \Rightarrow (( \sim p) \vee q)

is logically equivalent to:

View answer and explanation

Correct option: C

\sim (p \Rightarrow q)

Option C (

\sim (p \Rightarrow q)

) is correct because the negation of the given Boolean expression is logically equivalent to the negation of

p \Rightarrow q

115 Easy

115 of 232

Understanding +4 | -1

Consider the following statements.

I. "Every rectangle is a square" is a statement.

II. "Close the door" is not a statement.

Choose the correct option.

View answer and explanation

Correct option: C

Both are true

Option C (Both are true) is correct because the first statement is false, making it a statement, and the second statement is a command, thus not a statement.

116 Easy

116 of 232

Understanding +4 | -1

p:

Ram is smart

q:

Ram is intelligent
Then, the symbolic form Ram is smart and intelligent, is

View answer and explanation

Correct option: A

\left( {p \wedge q} \right)

Option A is correct because "and" is represented by the logical operator

\wedge

117 Easy

117 of 232

Understanding +4 | -1

Dual of

{\left( {x' \vee y'} \right)^\prime } = x \wedge y

View answer and explanation

Correct option: B

{\left( {x' \wedge y'} \right)^\prime } = x \vee y

Option B is correct because the dual of a statement is obtained by replacing

\wedge

with

\vee

\vee

with

\wedge

, 0 with 1, and 1 with 0.

118 Easy

118 of 232

Understanding +4 | -1

p \Rightarrow (q \vee r)

is false, then the truth values of p, q, r are respectively

View answer and explanation

Correct option: B

T, F, F

Option B (T, F, F) is correct because for the implication

p \Rightarrow (q \vee r)

to be false, p must be true and

(q \vee r)

must be false, which means both q and r must be false.

119 Easy

119 of 232

Understanding +4 | -1

For any two statements

p

and

q

, the negation of the expression

p \vee ( \sim p \wedge q)

View answer and explanation

Correct option: A

\sim p \wedge \sim q

Option A (

\sim p \wedge \sim q

) is correct because it represents the negation of the given expression after simplification using the distributive and De Morgan's laws.

120 Medium

120 of 232

Understanding +4 | -1

p

and

q

are two statements such that

p

: The question paper is easy.

q

: We shall pass.
Then, the symbolic statement

\sim p \rightarrow \sim q

means

View answer and explanation

Correct option: B

if the question paper is not easy, then we shall not pass

Option B (if the question paper is not easy, then we shall not pass) is the correct interpretation of the symbolic statement

\sim p \rightarrow \sim q

Revision notes and key takeaways

Review MATHEMATICAL REASONING in your textbook or class notes, then use this set to check your understanding.

Showing 91-120 of 232 questions

Your Progress

Mathematical reasoning practice · Mixed difficulty

Explore Other Chapters in MATHEMATICS

Continue Your Practice

Your practice