Mathematical Reasoning · Mathematics · JEE Main

Negation of $p \wedge(q \wedge \sim(p \wedge q))$ is :

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

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

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

The converse of $$((\sim p) \wedge q) \Rightarrow r$$ is

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

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

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

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

Among the statements (S1) : $$(p \Rightarrow q) \vee((\sim p) \wedge q)$$ is a tautology (S2) : $$(q \Rightarrow p) \Rightarrow((\sim p) \wedge q)$$ i...

Statement $$\mathrm{(P \Rightarrow Q) \wedge(R \Rightarrow Q)}$$ is logically equivalent to :

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 an 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

The number of ordered triplets of the truth values of $$p, q$$ and $$r$$ such that the truth value of the statement $$(p \vee q) \wedge(p \vee r) \Rig...

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$$\vee$$$$...

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