Q JEE MAIN 2021 S2

Which of the following is the negation of the statement "for all $M>0$, there exists $x \in S$ such that...

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Q JEE MAIN 2019

The Boolean expression ~ (p ⇒ (~ q)) is equivalent to

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Q JEE-MAIN 2019

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

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Q JEE Main 2020

The contrapositive of the statement “If I reach the station in time, then I will catch the train” is:

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Q JEE Main 2020

Let $X=\{x \in N: 1 \leq x \leq 17\}$ and $Y\{a x+b: x \in X$ and $...

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Q JEE MAIN 2019

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

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Q JEE MAIN 2020

Negation of the statement : ' $\sqrt{5}$ is an integer of 5 is irrational is

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Q JEE MAIN 2020

The mean and variance of 7 observations are 8 and 16, respectively. If five observations are 2, 4, 10, 12,...

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Q JEE MAIN 2020

The negation of the Boolean expression $x \leftrightarrow \sim y$ is equivalent to:

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Q JEE MAIN 2020

Consider the statement: "For an integer n , if $\mathrm{n}^3-1$ is even, then n is odd." The contrapositive statement of...

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Q JEE MAIN 2020

Which one of the following is a tautology?

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Q JEE MAIN 2019

The negation of the Boolean expression $\sim s \vee(\sim r \wedge s)$ is equivalent to:

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Q JEE MAIN 2020

Contrapositive of the statement : ‘If a function f is differentiable at a, then it is also continuous at a’,...

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Q JEE MAIN 2020

Given the following two statements: $\left(\mathrm{S}_1\right):(\mathrm{q} \vee \mathrm{p}) \rightarrow(\mathrm{p} \leftrightarrow \sim \mathrm{q})$ is a tautology: $...

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Q JEE MAIN 2020

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

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Q JEE MAIN 2020

Let $p, q, r$ be three statements such that the truth value of $(p \wedge q) \rightarrow(\sim q \vee r)$...

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Q JEE MAIN 2019

If $p \Rightarrow(q \vee r)$ is false, then truth values of $p, q, r$ are respectively:

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Q JEE MAIN 2020

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

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Q JEE Main 2021

Negation of the statement $(p \vee r) \Rightarrow(q \vee r)$ is :

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Q JEE MAIN 2021

Let *, □ $\in\{\wedge, \vee\}$ be such that the Boolean expression $\left(\mathrm{p}^* \sim q\right) \Rightarrow(\mathrm{p}$ □ q) is a tautology....

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Q JEE MAIN 2021

The statement $(p \wedge(p \rightarrow q) \wedge(q \rightarrow r)) \rightarrow r$ is :

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Q JEE Main 2021

If the truth value of the Boolean expression $((p \vee q) \wedge(q \rightarrow r) \wedge(\sim r)) \rightarrow(p \wedge q)$ is...

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Q JEE Main 2019

If the Boolean expression $(p \oplus q) \wedge(\sim p \odot q)$ is equivalent to $\mathbf{p} \wedge \mathbf{q}$, where $...

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Q JEE MAIN 2019

The contrapositive of the statement “If you are born in India, then you are a citizen of India”, is:

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Q JEE MAIN 2021

Consider the two statements : $(\mathrm{S} 1):(\mathrm{p} \rightarrow \mathrm{q}) \vee(\sim \mathrm{q} \rightarrow \mathrm{p})$ is a tautology. $...

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Q JEE MAIN_2021_

The Boolean expression $(P \Rightarrow q) \wedge(q \Rightarrow \sim p)$ is equivalent to:

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Q JEE MAIN 2019

Which one of the following statements is not a tautology?

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Q JEE MAIN 2021

The compound statement $(P \vee Q) \wedge(\sim P) \Rightarrow Q$ is equivalent of:

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Q JEE MAIN 2021

Let $F_1(A, B, C)=(A \wedge \sim B) \vee[\sim C \wedge(A \vee B)] \vee \sim A$ and $...

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Q JEE MAIN 2021

Consider the statement "The match will be played only if the weather is good and ground is not wet". Select...

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Q JEE MAIN 2021

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

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Q JEE-MAIN 2021

If the Boolean expression $(p \wedge q)(p \otimes q)$ is a tautology, then and $\otimes$ are respectively given by

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Q JEE MAIN 2021

The contrapositive of the statement "If you will work, you will earn money" is :

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Q JEE MAIN 2021

If P and Q are two statements, then which of the following compound statement is a tautology ?

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Q JEE MAIN_2021_

If the Boolean expression $(p=q) \Leftrightarrow\left(q^*(\sim p)\right)$ is a tautology, then the Boolean expression $\mathrm{p}^*(\sim \mathrm{q})$ is equivalent toni

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Q JEE MAIN 2021

Consider the following three statements : (A) If 3 + 3 = 7 then 4 + 3 = 8. (B)...

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Q JEE MAIN 2021

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

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Q JEE MAIN 2021

For the statements p and q, consider the following compound statements :\ Then which of the following statements is correct?

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Q JEE MAIN 2021

Which of the following Boolean expression is a tautology ?

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Q JEE MAIN 2021

The statement among the following that is a tautology is :

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Q JEE MAIN 2021

The statement $A \rightarrow(B \rightarrow A)$ is equivalent to :

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Q JEE MAIN_2022

The statement $(\sim(p \Leftrightarrow \sim q)) \wedge q$ is:

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Q JEE MAIN 2022

Which of the following statements is a tautology?

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Q JEE MAIN 2022

Which of the following statement is a tautology?

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Q JEE MAIN 2022

The maximum number of compound propositions, out of $...

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Q JEE MAIN 2022

Negation of the Boolean statement $(p \vee q) \Rightarrow((\sim r) \vee p)$ is equivalent to :

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Q JEE MAIN 2022

Let $\mathrm{A}=\left(\begin{array}{cc}2 & -1 \\ 0 & 2\end{array}\right)$. If $\mathrm{B}=1-{ }^5 \mathrm{C}_1(\operatorname{adj} \mathrm{~A})+{ }^5 \mathrm{C}_2(\operatorname{adj} \mathrm{~A})^2-\ldots \ldots-{ }^5 \mathrm{C}_5(\operatorname{adj} \mathrm{~A})^5$,...

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Q JEE MAIN 2022

Let $r \in\{p, q, \sim p, \sim q\}$ be such that the logical statement $...

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Q JEE MAIN 2022

Consider the following statements : A : Rishi is a judge. B : Rishi is honest. C : Rishi is...

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Q JEE MAIN 2022

The negation of the Boolean expression $((\sim q) \wedge p) \Rightarrow((\sim p) \vee q)$ is logically equivalent to

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Q JEE MAIN 2022

Let $\Delta \in\{\wedge, \vee, \Rightarrow, \Leftrightarrow\}$ be such that $(p \wedge q) \Delta((p \vee q) \Rightarrow q)$ is a tautology....

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Q JEE MAIN 2022

Let p, q, r be three logical statements. Consider the compound statements Then, which of the following is NOT true?

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Q JEE MAIN 2022

The Boolean expression $\left(\sim\left(p^{\wedge} q\right)\right) \vee q$ is equivalent to :

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Q JEE MAIN 2022

Let $\Delta, \nabla \in\{\wedge, \vee\}$ be such that $p \nabla q \Rightarrow((p \nabla q) \nabla r)$ is a tautology. Then...

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Q JEE MAIN 2022

The number of choices of $\Delta \in\{\wedge, \vee, \Rightarrow, \Leftrightarrow\}$, such that $...

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Q JEE MAIN 2022

Consider the following two propositions: If the proposition $p \rightarrow((\sim p) \vee q)$ is evaluated as FALSE, then:

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Q JEE-Main 2023

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

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Q JEE MAIN 2023

The statement (p ∧(~ q)∨ ((~ p)∧q)∨((~ p)∧(~ q)) is equivalent to

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Q JEE MAIN 2023

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

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Q JEE-Main 2023

Statement $(P \Rightarrow Q) \wedge(R \Rightarrow Q)$ is logically equivalent to

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Q JEE MAIN 2023

The negation of the statement $((A \wedge(B \vee C)) \Rightarrow(A \vee B)) \Rightarrow A$ is

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Q JEE MAIN 2023

Let $x_1, x_2$ $\_\_\_\_$ $x_{100}$ be in an arithmetic progression, with $x_1=2$ and their mean equal to 200 . If...

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Q JEE MAIN 2023

Among the two statements $(\mathrm{S} 1) \sim(\mathrm{p} \Rightarrow \mathrm{q}) \wedge(\mathrm{q} \wedge(\sim \mathrm{q}))$ is a contradiction and $$ (S 2) \sim(p...

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Q JEE-Main_2023

The negation of the statement $((A \wedge(B \vee C)) \Rightarrow(A \vee B)) \Rightarrow A$ is

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Q JEE MAIN 2023

Negation of $(p \Rightarrow q) \Rightarrow(q \Rightarrow p)$ is

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Q JEE MAIN 2023

Let sets A and B have 5 elements each. Let the mean of the elements in sets A and B...

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Q JEE MAIN 2023

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

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