Mathematical Reasoning * — JEE Main PYQs

109 previous year questions on Mathematical Reasoning * (Mathematics), newest first. Open any question for its complete step-by-step solution.

The negation of the statement $\sim p \land (p \lor q)$ is:
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For the statements $p$ and $q$ , consider the following compound statements:
(a) $(\sim q \land (p \to q)) \to\sim p$
(b) $((p \lor q) \land \sim p) \to q$

Then which of the following statements is correct?
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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 $5 + 6 = 17$ .

Then, which of the following statements is correct?
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The Boolean expression $(p \land q) \Rightarrow ((r \land q) \land p)$ is equivalent to:
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The statement $A \to (B \to A)$ is equivalent to :
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Which of the following Boolean expressions is not a tautology?
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The statement $(p \land (p \to q) \land (q \to r)) \to r$ is :
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Let $F_{1} (A, B, C) = (A \land \sim B) \lor [\sim C \land (A \lor B)] \lor \sim A$ and $F_{2} (A, B) = (A \lor B) \lor (B \to\sim A)$ be two logical expressions. Then :
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Negation of the statement $(p \lor r) \Rightarrow (q \lor r)$ is:
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Let $^{*}, Δ \in {\land, v}$ be such that the Boolean expression $(p^{*} \sim q) \Rightarrow (p Δ \sim q)$ is a tautology. Then :
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The compound statement $(P \lor Q) \land (\sim P) \Rightarrow Q$ is equivalent to :
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If the Boolean expression $(p \Rightarrow q) \Leftrightarrow (q * (\sim p))$ is a tautology, then the Boolean expression $p * (\sim q)$ is equivalent to:
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The Boolean expression $(p \Rightarrow q) \land (q \Rightarrow\sim p)$ is equivalent to:
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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 :
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Which of the following is the negation of the statement "for all $M > 0$ , there exists $x \in S$ such that $x \geq M$ "?
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Which of the following is equivalent to the Boolean expression $p \land \sim q$ ?
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Which of the following Boolean expression is a tautology?
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If $P$ and $Q$ are two statements, then which of the following compound statement is a tautology?
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If the Boolean expression $(p \land q) ⊙ (p \otimes q)$ is a tautology, then $⊙$ and $\otimes$ are respectively by:
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The logical statement $(p \Rightarrow q) \land (q \Rightarrow\sim p)$ is equivalent to:
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Let $A, B, C$ and $D$ be four non-empty sets. The contrapositive statement of "If $A \subseteq B$ and $B \subseteq D$ , then $A \subseteq C$ " is:
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Which one of the following is a tautology?
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Which of the following statement is a tautology?
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If $p \to (p \land \sim q)$ is false, then the truth values of $p$ and $q$ are respectively:
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Negation of the statement:
$5$ is an integer or 5 is irrational' is:
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The statement $(P \to (q \to p)) \to (p \to (p \lor q))$ is:
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The proposition $p \to\sim (p \land \sim q)$ is equivalent to:
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Let $p, q, r$ be three statements such that the truth value of $(p \land q) \to (\sim q \lor r)$ is $F$ . Then the truth values of $p, q, r$ are respectively:
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Consider the statement: "For an integer $n$ , if $n^{3} - 1$ is even, then $n$ is odd." The contrapositive statement of this statement is:
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The negation of the Boolean expression $x \leftrightarrow\sim y$ is equivalent to
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The negation of the Boolean expression $p \lor (\sim p \land q)$ is equivalent to:
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Given the following two statements:
$(S_{1}) : (q \lor p) \to (p \leftrightarrow\sim q)$ is a tautology.
$(S_{2}) :\sim q \land (\sim p \leftrightarrow q)$ is a fallacy. Then:
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Contrapositive of the statement:
'If a function f is differentiable at a, then it is also continuous at a', is:
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The contrapositive of the statement "If you are born in India, then you are a citizen of India", is:
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Which one of the following statements is not a tautology:
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For any two statements $p$ and $q$ , the negation of the expression $p \lor (\sim p \land q)$ is:
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Contrapositive of the statement "If two numbers are not equal, then their squares are not equal" is:
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If the truth value of the statement $p \to (\sim q \lor r)$ is false (F), then the truth values of the statement $p, q, r$ are respectively :
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The negation of the Boolean expression $\sim s \lor (\sim r \land s)$ is equivalent to
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If $q$ is false and $p \land q \leftrightarrow r$ is true, then which one of the following statements is a tautology?
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The Boolean expression $((p \land q) \lor (p \lor \sim q)) \land (\sim p \land \sim q)$ is equivalent to:
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The Boolean expression $\sim (p \Rightarrow (\sim q))$ is equivalent to:
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The expression $\sim (\sim p \to q)$ is logically equivalent to :
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If $P \Rightarrow (q \lor r)$ is false, then the truth values of $p, q, r$ are respectively
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The logical statement $[\sim (\sim p \lor q) \lor (p \land r) \land (\sim q \land r)]$ is equivalent to:
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If the Boolean expression $(p \oplus q) \land (\sim p Θ q)$ is equivalent to $p \land q$ , where $\oplus$ , $Θ \in {\land, \lor}$ , then the ordered pair $(\oplus, Θ)$ is :
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Which one of the following Boolean expressions is a tautology?
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The Boolean expression
$\sim (p \lor q) \lor (\sim p \land q)$ is equivalent to :
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The following statement
$(p \to q) \to [(\sim p \to q) \to q]$ is :
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The Boolean Expression $(p \land \sim q) \lor q \lor (\sim p \land q)$ is equivalent to:
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