List of top Mathematics Questions on mathematical reasoning asked in JEE Main

\(\begin{array}{l}(p \land r )\Leftrightarrow ( p \land (\sim q))\end{array}\)is equivalent to (~ p) when r is
Let r ∈ {p, q, ~p, ~q} be such that the logical statement r ∨ (~p) ⇒ (p ∧ q) ∨ r is a tautology. Then r is equal to :

Let\( Δ,▽∈{∧,∨} \)
be such that \(p▽q⇒((pΔq)▽r) \)
is a tautology. Then \((p▽q)Δr \)
is logically equivalent to:

The statement 
\((∼(p ⇔∼q))∧q \)
is :

Negation of the Boolean expression p⇔ (q⇒p) is
The statement (p∧q) ⇒ (p∧r) is equivalent to :
The negative of the statement $\sim p \wedge( p \vee q )$ is
Negation of the statement \((p \lor r) \implies (q \lor r)\) is :
Let \(*, \square \in \{\wedge, \vee\}\) be such that the Boolean expression \((p * \sim q) \implies (p \square q)\) is a tautology. Then :
The Boolean expression $(p \implies q) \wedge (q \implies \sim p)$ is equivalent to :
The contrapositive of the statement "If you will work, you will earn money" is:
For p and q, consider: (a) (~ q ∧ (p → q)) → ~ p, (b) ((p ∨ q) ∧ ~ p) → q. Which is correct ?
Consider the two statements :
(S1) : \((p \to q) \lor (\neg q \to p)\) is a tautology.
(S2) : \((p \land \neg q) \land (\neg p \lor q)\) is a fallacy.
Then :
If the truth value of the Boolean expression \(((p \vee q) \wedge (q \to r) \wedge (\sim r)) \to (p \wedge q)\) is false, then the truth values of the statements \(p, q, r\) respectively can be :
The statement $(p \land (p \to q) \land (q \to r)) \to r$ is :
The Boolean expression \((p \land q) \Rightarrow ((r \land q) \land p)\) is equivalent to :
The compound statement $(P \lor Q) \land (\sim P) \Rightarrow Q$ is equivalent to :
The statement A → (B → A) is equivalent to :
The statement among the following that is a tautology is :
If P and Q are two statements, then which of the following compound statement is a tautology ?
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 negation of the statement ~p ∧ (p ∨ q) is :
Which one of the following is a tautology ?
Which of the following statements is a tautology?
The logical statement $[\sim (\sim p \vee q) \vee (p \wedge r) \wedge (\sim q \wedge r)]$ is equivalent to: