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## Mathematical Reasoning

### Mathematics

#### Previous Years Questions

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The statement $$(p \Rightarrow q) \vee(p \Rightarrow r)$$ is NOT equivalent to
JEE Main 2022 (Online) 29th July Evening Shift
The statement $$(p \wedge q) \Rightarrow(p \wedge r)$$ is equivalent to :
JEE Main 2022 (Online) 29th July Morning Shift
Let $$\mathrm{p}$$ : Ramesh listens to music. $$\mathrm{q}$$ : Ramesh is out of his village. $$\mathrm{r}$$ : It is Sund...
JEE Main 2022 (Online) 28th July Evening Shift
Let the operations $$*, \odot \in\{\wedge, \vee\}$$. If $$(\mathrm{p} * \mathrm{q}) \odot(\mathrm{p}\, \odot \sim \mathr... JEE Main 2022 (Online) 28th July Morning Shift If the truth value of the statement$$(P \wedge(\sim R)) \rightarrow((\sim R) \wedge Q)$$is F, then the truth value of ... JEE Main 2022 (Online) 27th July Evening Shift$$(p \wedge r) \Leftrightarrow(p \wedge(\sim q))$$is equivalent to$$(\sim p)$$when$$r$$is JEE Main 2022 (Online) 27th July Morning Shift Negation of the Boolean expression$$p \Leftrightarrow(q \Rightarrow p)$$is JEE Main 2022 (Online) 26th July Evening Shift The statement$$(\sim(\mathrm{p} \Leftrightarrow \,\sim \mathrm{q})) \wedge \mathrm{q}$$is : JEE Main 2022 (Online) 26th July Morning Shift Consider the following statements: P : Ramu is intelligent. Q : Ramu is rich. R : Ramu is not honest. The negation of th... JEE Main 2022 (Online) 25th July Evening Shift Which of the following statements is a tautology ? JEE Main 2022 (Online) 25th July Morning Shift The conditional statement$$((p \wedge q) \to (( \sim p) \vee r)) \vee ((( \sim p) \vee r) \to (p \wedge q))$$is :... JEE Main 2022 (Online) 30th June Morning Shift The number of choices for$$\Delta \in \{ \wedge , \vee , \Rightarrow , \Leftrightarrow \} $$, such that$$(p\Delta q)...
JEE Main 2022 (Online) 24th June Morning Shift
Consider the following statements: A : Rishi is a judge. B : Rishi is honest. C : Rishi is not arrogant. The negation of...
JEE Main 2022 (Online) 24th June Evening Shift
Consider the following two propositions: $$P1: \sim (p \to \sim q)$$ $$P2:(p \wedge \sim q) \wedge (( \sim p) \vee q)... JEE Main 2022 (Online) 25th June Morning Shift The negation of the Boolean expression (($$\sim$$q)$$\wedge$$p)$$\Rightarrow$$(($$\sim$$p)$$\vee$$q) is logicall... JEE Main 2022 (Online) 25th June Evening Shift Let r$$\in$${p, q,$$\sim$$p,$$\sim$$q} be such that the logical statement r$$\vee$$($$\sim$$p)$$\Rightarrow$$(p ... JEE Main 2022 (Online) 26th June Evening Shift Let$$\Delta$$,$$\nabla \in$${$$\wedge$$,$$\vee$$} be such that p$$\nabla$$q$$\Rightarrow$$((p$$\Delta$$q)... JEE Main 2022 (Online) 26th June Morning Shift The boolean expression$$( \sim (p \wedge q)) \vee q$$is equivalent to : JEE Main 2022 (Online) 27th June Morning Shift Which of the following statement is a tautology? JEE Main 2022 (Online) 27th June Evening Shift Let p, q, r be three logical statements. Consider the compound statements$${S_1}:(( \sim p) \vee q) \vee (( \sim p) \ve...
JEE Main 2022 (Online) 28th June Morning Shift
Negation of the Boolean statement (p $$\vee$$ q) $$\Rightarrow$$ (($$\sim$$ r) $$\vee$$ p) is equivalent to
JEE Main 2022 (Online) 29th June Evening Shift
Let $$\Delta$$ $$\in$$ {$$\wedge$$, $$\vee$$, $$\Rightarrow$$, $$\Leftrightarrow$$} be such that (p $$\wedge$$ q) $$\Del... JEE Main 2022 (Online) 29th June Morning Shift Which of the following is equivalent to the Boolean expression p$$\wedge\sim$$q ? JEE Main 2021 (Online) 1st September Evening Shift Negation of the statement (p$$\vee$$r)$$\Rightarrow$$(q$$\vee$$r) is : JEE Main 2021 (Online) 31st August Evening Shift Let *, ▢$$\in$${$$\wedge$$,$$\vee$$} be such that the Boolean expression (p *$$\sim$$q)$$\Rightarrow$$(p ▢ q) is a... JEE Main 2021 (Online) 31st August Morning Shift The Boolean expression (p$$\wedge$$q)$$\Rightarrow$$((r$$\wedge$$q)$$\wedge$$p) is equivalent to : JEE Main 2021 (Online) 27th August Evening Shift The statement (p$$ \wedge $$(p$$\to$$q)$$\wedge$$(q$$\to$$r))$$\to$$r is : JEE Main 2021 (Online) 27th August Morning Shift Consider the two statements :(S1) : (p$$\to$$q)$$ \vee $$($$ \sim $$q$$\to$$p) is a tautology .(S2) : (p$$ \wedg...
JEE Main 2021 (Online) 26th August Evening Shift
If the truth value of the Boolean expression $$\left( {\left( {p \vee q} \right) \wedge \left( {q \to r} \right) \wedge ... JEE Main 2021 (Online) 26th August Morning Shift The compound statement$$(P \vee Q) \wedge ( \sim P) \Rightarrow Q$$is equivalent to : JEE Main 2021 (Online) 27th July Morning Shift Consider the statement "The match will be played only if the weather is good and ground is not wet". Select the correct ... JEE Main 2021 (Online) 25th July Evening Shift Which of the following is the negation of the statement "for all M &gt; 0, there exists x$$\in$$S such that x$$\ge$$M"... JEE Main 2021 (Online) 27th July Evening Shift The Boolean expression$$(p \Rightarrow q) \wedge (q \Rightarrow \sim p)$$is equivalent to : JEE Main 2021 (Online) 25th July Morning Shift Which of the following Boolean expressions is not a tautology? JEE Main 2021 (Online) 22th July Evening Shift Consider the following three statements :(A) If 3 + 3 = 7 then 4 + 3 = 8(B) If 5 + 3 = 8 then earth is flat.(C) If both ... JEE Main 2021 (Online) 20th July Evening Shift The Boolean expression$$(p \wedge \sim q) \Rightarrow (q \vee \sim p)$$is equivalent to : JEE Main 2021 (Online) 20th July Morning Shift If P and Q are two statements, then which of the following compound statement is a tautology? JEE Main 2021 (Online) 18th March Evening Shift If the Boolean expression$$(p \wedge q) \odot (p \otimes q)$$is a tautology, then$$ \odot $$and$$ \otimes $$are re... JEE Main 2021 (Online) 17th March Evening Shift If the Boolean expression (p$$ \Rightarrow $$q)$$ \Leftrightarrow $$(q * ($$ \sim $$q) is a tautology, then the bool... JEE Main 2021 (Online) 17th March Morning Shift Which of the following Boolean expression is a tautology? JEE Main 2021 (Online) 16th March Morning Shift Let F1(A, B, C) = (A$$ \wedge  \sim $$B)$$ \vee $$[$$\sim$$C$$\wedge$$(A$$\vee$$B)]$$\vee\sim$$A and... JEE Main 2021 (Online) 26th February Evening Shift The contrapositive of the statement "If you will work, you will earn money" is : JEE Main 2021 (Online) 25th February Evening Shift The statement A$$ \to $$(B$$ \to $$A) is equivalent to : JEE Main 2021 (Online) 25th February Morning Slot For the statements p and q, consider the following compound statements :(a)$$( \sim q \wedge (p \to q)) \to \sim p$$(b... JEE Main 2021 (Online) 24th February Evening Slot The negation of the statement$$ \sim p \wedge (p \vee q)$$is : JEE Main 2021 (Online) 24th February Evening Slot The statement among the following that is a tautology is : JEE Main 2021 (Online) 24th February Morning Slot Consider the statement : ‘‘For an integer n, if n3 – 1 is even, then n is odd.’’ The contrapositive statement of this st... JEE Main 2020 (Online) 6th September Evening Slot The negation of the Boolean expression p$$ \vee $$(~p$$ \wedge $$q) is equivalent to : JEE Main 2020 (Online) 6th September Morning Slot The statement$$\left( {p \to \left( {q \to p} \right)} \right) \to \left( {p \to \left( {p \vee q} \right)} \right)$$i... JEE Main 2020 (Online) 5th September Evening Slot The negation of the Boolean expression x$$ \leftrightarrow $$~ y is equivalent to : JEE Main 2020 (Online) 5th September Morning Slot Contrapositive of the statement : ‘If a function f is differentiable at a, then it is also continuous at a’, is: JEE Main 2020 (Online) 4th September Evening Slot Given the following two statements:$$\left( {{S_1}} \right):\left( {q \vee p} \right) \to \left( {p \leftrightarrow \s...
JEE Main 2020 (Online) 4th September Morning Slot
Let p, q, r be three statements such that the truth value of (p $$\wedge$$ q) $$\to$$ ($$\sim$$q $$\vee$$ r) is ...
JEE Main 2020 (Online) 3rd September Evening Slot
The proposition p $$\to$$ ~ (p $$\wedge$$ ~q) is equivalent to :
JEE Main 2020 (Online) 3rd September Morning Slot
Which of the following is a tautology ?
JEE Main 2020 (Online) 2nd September Evening Slot
The contrapositive of the statement "If I reach the station in time, then I will catch the train" is :
JEE Main 2020 (Online) 2nd September Morning Slot
If p $$\to$$ (p $$\wedge$$ ~q) is false, then the truth values of p and q are respectively :
JEE Main 2020 (Online) 9th January Evening Slot
Negation of the statement : $$\sqrt 5$$ is an integer or 5 is irrational is :
JEE Main 2020 (Online) 9th January Morning Slot
Which of the following statements is a tautology?
JEE Main 2020 (Online) 8th January Evening Slot
Which one of the following is a tautology?
JEE Main 2020 (Online) 8th January Morning Slot
Let A, B, C and D be four non-empty sets. The contrapositive statement of "If A $$\subseteq$$ B and B $$\subseteq$$ ...
JEE Main 2020 (Online) 7th January Evening Slot
The logical statement (p $$\Rightarrow$$ q) $$\Lambda$$ ( q $$\Rightarrow$$ ~p) is equivalent to:
JEE Main 2020 (Online) 7th January Morning Slot
The Boolean expression ~(p $$\Rightarrow$$ (~q)) is equivalent to :
JEE Main 2019 (Online) 12th April Evening Slot
If the truth value of the statement p $$\to$$ (~q $$\vee$$ r) is false (F), then the truth values of the statements ...
JEE Main 2019 (Online) 12th April Morning Slot
The negation of the Boolean expression ~ s $$\vee$$ (~r $$\wedge$$ s) is equivalent to :
JEE Main 2019 (Online) 10th April Evening Slot
Which one of the following Boolean expressions is a tautology ?
JEE Main 2019 (Online) 10th April Morning Slot
If p $$\Rightarrow$$ (q $$\vee$$ r) is false, then the truth values of p, q, r are respectively :-
JEE Main 2019 (Online) 9th April Evening Slot
For any two statements p and q, the negation of the expression p $$\vee$$ (~p $$\wedge$$ q) is
JEE Main 2019 (Online) 9th April Morning Slot
Which one of the following statements is not a tautology ?
JEE Main 2019 (Online) 8th April Evening Slot
The contrapositive of the statement "If you are born in India, then you are a citizen of India", is :
JEE Main 2019 (Online) 8th April Morning Slot
The expression $$\sim$$ ($$\sim$$ p $$\to$$ q) is logically equivalent to :
JEE Main 2019 (Online) 12th January Evening Slot
The Boolean expression ((p $$\wedge$$ q) $$\vee$$ (p $$\vee$$ $$\sim$$ q)) $$\wedge$$ ($$\sim$$ p $$\wedge ... JEE Main 2019 (Online) 12th January Morning Slot Contrapositive of the statement " If two numbers are not equal, then their squares are not equal." is : JEE Main 2019 (Online) 11th January Evening Slot If q is false and p$$ \wedge $$q$$ \leftrightarrow $$r is true, then which one of the following statements is a tau... JEE Main 2019 (Online) 11th January Morning Slot Consider the following three statements : P : 5 is a prime number Q : 7 is a factor of 192 R : L.C.M. of 5 and 7 is 35 T... JEE Main 2019 (Online) 10th January Evening Slot Consider the statement : "P(n) : n2 – n + 41 is prime". Then which one of the following is true ? JEE Main 2019 (Online) 10th January Morning Slot The logical statement [$$ \sim $$($$ \sim $$p$$ \vee $$q)$$ \vee $$(p$$ \wedge $$r)]$$ \wedge $$($$ \sim $$... JEE Main 2019 (Online) 9th January Evening Slot If the Boolean expression (p$$ \oplus $$q)$$\wedge$$(~ p$$ \odot $$q) is equivalent to p$$\wedge$$q, where ... JEE Main 2019 (Online) 9th January Morning Slot If p$$ \to $$($$ \sim $$p$$ \vee  \sim $$q) is false, then the truth values of p and q are respectively : JEE Main 2018 (Online) 16th April Morning Slot Consider the following two statements : Statement p : The value of sin 120o can be derived by taking$$\theta = {240^o...
JEE Main 2018 (Online) 15th April Evening Slot
If (p $$\wedge$$ $$\sim$$ q) $$\wedge$$ (p $$\wedge$$ r) $$\to$$ $$\sim$$ p $$\vee$$ q is false, then the ...
JEE Main 2018 (Online) 15th April Morning Slot
The Boolean expression $$\sim \left( {p \vee q} \right) \vee \left( { \sim p \wedge q} \right)$$ is equvalent to...
JEE Main 2018 (Offline)
Contrapositive of the statement ‘If two numbers are not equal, then their squares are not equal’, is :
JEE Main 2017 (Online) 9th April Morning Slot
The proposition $$\left( { \sim p} \right) \vee \left( {p \wedge \sim q} \right)$$ is equivalent to :
JEE Main 2017 (Online) 8th April Morning Slot
The following statement $$\left( {p \to q} \right) \to \left[ {\left( { \sim p \to q} \right) \to q} \right]$$ is...
JEE Main 2017 (Offline)
The contrapositive of the following statement, “If the side of a square doubles, then its area increases four times”, i...
JEE Main 2016 (Online) 10th April Morning Slot
Consider the following two statements : P : &nbsp;&nbsp;&nbsp; If 7 is an odd number, then 7 is divisible by 2. Q :&nbs...
JEE Main 2016 (Online) 9th April Morning Slot
The Boolean expression $$\left( {p \wedge \sim q} \right) \vee q \vee \left( { \sim p \wedge q} \right)$$ is equivalent...
JEE Main 2016 (Offline)
The negation of $$\sim s \vee \left( { \sim r \wedge s} \right)$$ is equivalent to
JEE Main 2015 (Offline)
The statement $$\sim \left( {p \leftrightarrow \sim q} \right)$$ is
JEE Main 2014 (Offline)
Consider : Statement − I : $$\left( {p \wedge \sim q} \right) \wedge \left( { \sim p \wedge q} \right)$$ is a fallacy. ...
JEE Main 2013 (Offline)
The negation of the statement “If I become a teacher, then I will open a school” is
AIEEE 2012
Consider the following statements P : Suman is brilliant Q : Suman is rich R : Suman is honest The negation of the s...
AIEEE 2011
Let S be a non-empty subset of R. Consider the following statement: P : There is a rational number x ∈ S such that x &gt...
AIEEE 2010
Statement-1 : $$\sim \left( {p \leftrightarrow \sim q} \right)$$ is equivalent to $${p \leftrightarrow q}$$. Statement...
AIEEE 2009
The statement $$p \to \left( {q \to p} \right)$$ is equivalent to
AIEEE 2008
Let p be the statement “x is an irrational number”, q be the statement “y is a transcendental number”, and r be the stat...
AIEEE 2008

## Numerical

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The maximum number of compound propositions, out of p$$\vee$$r$$\vee$$s, p$$\vee$$r$$\vee$$$$\sim$$s, p$$\vee$$$$\sim$$q...
JEE Main 2022 (Online) 28th June Evening Shift

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