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Class XI Maths Reasoning & Induction 1

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Question 1

The negation of ~ s ∨ (~r ∧ s) is equivalent to :

Question 2

The Boolean Expression

is equivalent to :

Question 3

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 statements is the negation of the statement P?

Question 4

Directions: Assertion– Reason type questions. Each of these questions contains two statements;

Statement – 1 (Assertion) and

Statement – 2 (Reason)

Each of these questions also have four alternative choices, only one of which is the correct answer. You have to select the correct choice.

Statement 1: ~ (p ↔ ~ q) is equivalent to p ↔ q
Statement 2 : ~ (p ↔ ~ q) is a tautology

Question 5

Consider the following statements -
Statement − I : (p ∧ ~ q) ∧ (~ p ∧ q) is a fallacy.
Statement − II : (p → q) ↔ (~ q → ~ p) is a tautology.

Question 6

If A =

and I =

, then which one of the following holds for all n ≥ 1, by the principle of mathematical induction

Question 7

The statement p → (q → p) is equivalent to

Question 8

If x > –1, then the statement (1 + x)ⁿ > 1+nx is true for

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Apr 1JEE & BITSAT