JEE Main
Mathematics
Mathematical Reasoning
Previous Years Questions

Which of the following statements is a tautology?
The negation of the expression $$q \vee \left( {( \sim \,q) \wedge p} \right)$$ is equivalent to
The number of values of $\mathrm{r} \in\{\mathrm{p}, \mathrm{q}, \sim \mathrm{p}, \sim \mathrm{q}\}$ for which $((\mathrm{p} \wedge \mathrm{q}) \Right... $$(\mathrm{S} 1)~(p \Rightarrow q) \vee(p \wedge(\sim q))$$ is a tautology $$(\mathrm{S} 2)~((\sim p) \Rightarrow(\sim q)) \wedge((\sim p) \vee q)$$ i... Consider the following statements: P : I have fever Q: I will not take medicine$\mathrm{R}$: I will take rest. The statement "If I have fever, then ... Among the statements : $$(\mathrm{S} 1)~((\mathrm{p} \vee \mathrm{q}) \Rightarrow \mathrm{r}) \Leftrightarrow(\mathrm{p} \Rightarrow \mathrm{r})$$ $$(... If$$p,q$$and$$r$$are three propositions, then which of the following combination of truth values of$$p,q$$and$$r$$makes the logical expression... Let$$\Delta ,\nabla \in \{ \wedge , \vee \} $$be such that$$\mathrm{(p \to q)\Delta (p\nabla q)}$$is a tautology. Then The statement$$\left( {p \wedge \left( { \sim q} \right)} \right) \Rightarrow \left( {p \Rightarrow \left( { \sim q} \right)} \right)$$is Let p and q be two statements. Then$$ \sim \left( {p \wedge (p \Rightarrow \, \sim q)} \right)$$is equivalent to The compound statement$$\left( { \sim (P \wedge Q)} \right) \vee \left( {( \sim P) \wedge Q} \right) \Rightarrow \left( {( \sim P) \wedge ( \sim Q)} ... The statement $$(p \Rightarrow q) \vee(p \Rightarrow r)$$ is NOT equivalent to The statement $$(p \wedge q) \Rightarrow(p \wedge r)$$ is equivalent to : Let $$\mathrm{p}$$ : Ramesh listens to music. $$\mathrm{q}$$ : Ramesh is out of his village. $$\mathrm{r}$$ : It is Sunday. $$\mathrm{s}$$ : It is Sat... Let the operations $$*, \odot \in\{\wedge, \vee\}$$. If $$(\mathrm{p} * \mathrm{q}) \odot(\mathrm{p}\, \odot \sim \mathrm{q})$$ is a tautology, then t... If the truth value of the statement $$(P \wedge(\sim R)) \rightarrow((\sim R) \wedge Q)$$ is F, then the truth value of which of the following is $$\m...$$(p \wedge r) \Leftrightarrow(p \wedge(\sim q))$$is equivalent to$$(\sim p)$$when$$r$$is Negation of the Boolean expression$$p \Leftrightarrow(q \Rightarrow p)$$is The statement$$(\sim(\mathrm{p} \Leftrightarrow \,\sim \mathrm{q})) \wedge \mathrm{q}$$is : Consider the following statements: P : Ramu is intelligent. Q : Ramu is rich. R : Ramu is not honest. The negation of the statement "Ramu is intellige... Which of the following statements is a tautology ? The conditional statement$$((p \wedge q) \to (( \sim p) \vee r)) \vee ((( \sim p) \vee r) \to (p \wedge q))$$is : Negation of the Boolean statement (p$$\vee$$q)$$\Rightarrow$$(($$\sim$$r)$$\vee$$p) is equivalent to Let$$\Delta\in$${$$\wedge$$,$$\vee$$,$$\Rightarrow$$,$$\Leftrightarrow$$} be such that (p$$\wedge$$q)$$\Delta$$((p$$\vee$$q)$$\Righta... Let p, q, r be three logical statements. Consider the compound statements $${S_1}:(( \sim p) \vee q) \vee (( \sim p) \vee r)$$ and $${S_2}:p \to (q \v... Which of the following statement is a tautology? The boolean expression$$( \sim (p \wedge q)) \vee q$$is equivalent to : Let r$$\in$${p, q,$$\sim$$p,$$\sim$$q} be such that the logical statement r$$\vee$$($$\sim$$p)$$\Rightarrow$$(p$$\wedge$$q)$$\vee$$r is a ... Let$$\Delta$$,$$\nabla \in$${$$\wedge$$,$$\vee$$} be such that p$$\nabla$$q$$\Rightarrow$$((p$$\Delta$$q)$$\nabla$$r) is a tautology.... The negation of the Boolean expression (($$\sim$$q)$$\wedge$$p)$$\Rightarrow$$(($$\sim$$p)$$\vee$$q) is logically equivalent to : Consider the following two propositions:$$P1: \sim (p \to \sim q)P2:(p \wedge \sim q) \wedge (( \sim p) \vee q)$$If the proposition$$p \to (... Consider the following statements: A : Rishi is a judge. B : Rishi is honest. C : Rishi is not arrogant. The negation of the statement "if Rishi is a ... The number of choices for $$\Delta \in \{ \wedge , \vee , \Rightarrow , \Leftrightarrow \}$$, such that $$(p\Delta q) \Rightarrow ((p\Delta \sim q... Which of the following is equivalent to the Boolean expression p$$\wedge\sim$$q ? Negation of the statement (p$$\vee$$r)$$\Rightarrow$$(q$$\vee$$r) is : Let *, ▢$$\in$${$$\wedge$$,$$\vee$$} be such that the Boolean expression (p *$$\sim$$q)$$\Rightarrow$$(p ▢ q) is a tautology. Then : The Boolean expression (p$$\wedge$$q)$$\Rightarrow$$((r$$\wedge$$q)$$\wedge$$p) is equivalent to : The statement (p$$ \wedge $$(p$$\to$$q)$$\wedge$$(q$$\to$$r))$$\to$$r is : Consider the two statements :(S1) : (p$$\to$$q)$$ \vee $$($$ \sim $$q$$\to$$p) is a tautology .(S2) : (p$$ \wedge  \sim $$q)$$ \wedge$...
If the truth value of the Boolean expression $$\left( {\left( {p \vee q} \right) \wedge \left( {q \to r} \right) \wedge \left( { \sim r} \right)} \rig... Which of the following is the negation of the statement "for all M > 0, there exists x$$\in$$S such that x$$\ge$$M" ? The compound statement$$(P \vee Q) \wedge ( \sim P) \Rightarrow Q$$is equivalent to : Consider the statement "The match will be played only if the weather is good and ground is not wet". Select the correct negation from the following : The Boolean expression$$(p \Rightarrow q) \wedge (q \Rightarrow \sim p)$$is equivalent to : Which of the following Boolean expressions is not a tautology? Consider the following three statements :(A) If 3 + 3 = 7 then 4 + 3 = 8(B) If 5 + 3 = 8 then earth is flat.(C) If both (A) and (B) are true then 5 + ... The Boolean expression$$(p \wedge \sim q) \Rightarrow (q \vee \sim p)$$is equivalent to : If P and Q are two statements, then which of the following compound statement is a tautology? If the Boolean expression$$(p \wedge q) \odot (p \otimes q)$$is a tautology, then$$ \odot $$and$$ \otimes $$are respectively given by : If the Boolean expression (p$$ \Rightarrow $$q)$$ \Leftrightarrow $$(q * ($$ \sim $$p) is a tautology, then the boolean expression (p * ($$ \sim $... Which of the following Boolean expression is a tautology? Let F1(A, B, C) = (A $$\wedge$$ $$\sim$$ B) $$\vee$$ [$$\sim$$C $$\wedge$$ (A $$\vee$$ B)] $$\vee$$ $$\sim$$ A and F2(A, B) = (A $$\vee$$ B) $$\... The contrapositive of the statement "If you will work, you will earn money" is : The statement A$$ \to $$(B$$ \to $$A) is equivalent to : The negation of the statement$$ \sim p \wedge (p \vee q)$$is : For the statements p and q, consider the following compound statements :(a)$$( \sim q \wedge (p \to q)) \to \sim p$$(b)$$((p \vee q) \wedge \sim p... The statement among the following that is a tautology is : Consider the statement : ‘‘For an integer n, if n3 – 1 is even, then n is odd.’’ The contrapositive statement of this statement is : ... The negation of the Boolean expression p $$\vee$$ (~p $$\wedge$$ q) is equivalent to : The statement $$\left( {p \to \left( {q \to p} \right)} \right) \to \left( {p \to \left( {p \vee q} \right)} \right)$$ is : The negation of the Boolean expression x $$\leftrightarrow$$ ~ y is equivalent to : Contrapositive of the statement : ‘If a function f is differentiable at a, then it is also continuous at a’, is: Given the following two statements: $$\left( {{S_1}} \right):\left( {q \vee p} \right) \to \left( {p \leftrightarrow \sim q} \right)$$ is a tautology... Let p, q, r be three statements such that the truth value of (p $$\wedge$$ q) $$\to$$ ($$\sim$$q $$\vee$$ r) is F. Then the truth values of p,... The proposition p $$\to$$ ~ (p $$\wedge$$ ~q) is equivalent to : Which of the following is a tautology ? The contrapositive of the statement "If I reach the station in time, then I will catch the train" is : If p $$\to$$ (p $$\wedge$$ ~q) is false, then the truth values of p and q are respectively : Negation of the statement : $$\sqrt 5$$ is an integer or 5 is irrational is : Which of the following statements is a tautology? Which one of the following is a tautology? Let A, B, C and D be four non-empty sets. The contrapositive statement of "If A $$\subseteq$$ B and B $$\subseteq$$ D, then A $$\subseteq$$ C" i... The logical statement (p $$\Rightarrow$$ q) $$\Lambda$$ ( q $$\Rightarrow$$ ~p) is equivalent to: The Boolean expression ~(p $$\Rightarrow$$ (~q)) is equivalent to : If the truth value of the statement p $$\to$$ (~q $$\vee$$ r) is false (F), then the truth values of the statements p, q, r are respectively : The negation of the Boolean expression ~ s $$\vee$$ (~r $$\wedge$$ s) is equivalent to : Which one of the following Boolean expressions is a tautology ? If p $$\Rightarrow$$ (q $$\vee$$ r) is false, then the truth values of p, q, r are respectively :- For any two statements p and q, the negation of the expression p $$\vee$$ (~p $$\wedge$$ q) is Which one of the following statements is not a tautology ? The contrapositive of the statement "If you are born in India, then you are a citizen of India", is : The expression $$\sim$$ ($$\sim$$ p $$\to$$ q) is logically equivalent to : The Boolean expression ((p $$\wedge$$ q) $$\vee$$ (p $$\vee$$ $$\sim$$ q)) $$\wedge$$ ($$\sim$$ p $$\wedge$$ $$\sim$$ q) is equivalent... Contrapositive of the statement " If two numbers are not equal, then their squares are not equal." is : If q is false and p $$\wedge$$ q $$\leftrightarrow$$ r is true, then which one of the following statements is a tautology ? 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 Then the truth value of which o... Consider the statement : "P(n) : n2 – n + 41 is prime". Then which one of the following is true ? The logical statement [ $$\sim$$ ( $$\sim$$ p $$\vee$$ q) $$\vee$$ (p $$\wedge$$ r)] $$\wedge$$ ($$\sim$$ q $$\wedge$$ r) is equivalen... If the Boolean expression (p $$\oplus$$ q) $$\wedge$$ (~ p $$\odot$$ q) is equivalent to p $$\wedge$$ q, where $$\oplus , \odot \in \left\{ ... If p$$ \to $$($$ \sim $$p$$ \vee  \sim $$q) is false, then the truth values of p and q are respectively : The Boolean expression$$ \sim \left( {p \vee q} \right) \vee \left( { \sim p \wedge q} \right)$$is equvalent to Consider the following two statements : Statement p : The value of sin 120o can be derived by taking$$\theta = {240^o}$$in the equation 2sin$${\... If (p $$\wedge$$ $$\sim$$ q) $$\wedge$$ (p $$\wedge$$ r) $$\to$$ $$\sim$$ p $$\vee$$ q is false, then the truth values of $$p, q$$ and$...
Contrapositive of the statement ‘If two numbers are not equal, then their squares are not equal’, is :
The proposition $$\left( { \sim p} \right) \vee \left( {p \wedge \sim q} \right)$$ is equivalent to :
The following statement $$\left( {p \to q} \right) \to \left[ {\left( { \sim p \to q} \right) \to q} \right]$$ is
The contrapositive of the following statement, “If the side of a square doubles, then its area increases four times”, is :
Consider the following two statements : P :     If 7 is an odd number, then 7 is divisible by 2. Q :    If 7 is a prime...
The Boolean expression $$\left( {p \wedge \sim q} \right) \vee q \vee \left( { \sim p \wedge q} \right)$$ is equivalent to
The negation of $$\sim s \vee \left( { \sim r \wedge s} \right)$$ is equivalent to
The statement $$\sim \left( {p \leftrightarrow \sim q} \right)$$ is
Consider : Statement − I : $$\left( {p \wedge \sim q} \right) \wedge \left( { \sim p \wedge q} \right)$$ is a fallacy. Statement − II :$$\left( {p \t... The negation of the statement “If I become a teacher, then I will open a school” is Consider the following statements P : Suman is brilliant Q : Suman is rich R : Suman is honest The negation of the statement, “Suman is brilliant ... Let S be a non-empty subset of R. Consider the following statement: P : There is a rational number x ∈ S such that x > 0. Which of the following st... Statement-1 :$$ \sim \left( {p \leftrightarrow \sim q} \right)$$is equivalent to$${p \leftrightarrow q}$$. Statement-2 :$$ \sim \left( {p \leftri...
Let p be the statement “x is an irrational number”, q be the statement “y is a transcendental number”, and r be the statement “x is a rational number ...
The statement $$p \to \left( {q \to p} \right)$$ is equivalent to

## MCQ (More than One Correct Answer)

The statement $$B \Rightarrow \left( {\left( { \sim A} \right) \vee B} \right)$$ is equivalent to :

## Numerical

The maximum number of compound propositions, out of p$$\vee$$r$$\vee$$s, p$$\vee$$r$$\vee$$$$\sim$$s, p$$\vee$$$$\sim$$q$$\vee$$s, $$\sim$$p$$\vee$$...
EXAM MAP
Joint Entrance Examination