JEE Advanced Mathematics: Mathematical Reasoning Practice Questions

12 questions with answers and step-by-step solutions. Tap any question to see the full worked solution.

Q1.
$The statement p and (q or r) is logically equivalent to which of the following?$
Easy
Q2.
$Which of the following is the inverse of the statement: If x is a prime number, then x is odd?$
Easy
Q3.
$What is the negation of the statement: For all real numbers x, x squared is greater than or equal to zero?$
Easy
Q4.
$C o n s i d er t h es t a t e m e n tP : F or e v er y r e a l n u mb er x, i f x^{2} i s g r e a t er t han 0, t h e n x i s n o t e q u a l t o 0. W hi c h o f t h e f o l l o w in g i s t h e n e g a t i o n o f P ?$
Medium
Q5.
$Let p and q be two propositions. The compound statement (p or q) and (not p or q) is logically equivalent to which of the following?$
Medium
Q6.
$The contrapositive of the statement 'If a function f is differentiable at x = a, then f is continuous at x = a' is:$
Medium
Q7.
$The statement 'If x is a prime number, then x is odd' is false. Which of the following is a counterexample?$
Medium
Q8.
$Which of the following logical statements is a tautology?$
Hard
Q9.
$Identify the contrapositive of the statement: If a function f is differentiable at x = a, then f is continuous at x = a.$
Hard
Q10.
$Let p and q be propositions. Which of the following logical expressions is equivalent to the implication p implies q?$
Hard
Q11.
$Determine the truth value of the statement: For all real numbers x, x squared is greater than or equal to 0, and there exists a real number x such that x square$
Hard
Q12.
$Consider the statement P: For every real number x, there exists a real number y such that x + y = 0. Determine the truth value of the negation of P.$
Hard

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