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NCERT Class 12 Maths Chapter 1: Relations And Functions 7 Questions Solved

NCERT Solutions for Class 12 Maths Chapter 1 Relations And Functions — Miscellaneous Exercise

Click any question below for its step-by-step NCERT textbook solution, concept hints, and worked explanation.

Prove that f:ℝ→(−1,1), f(x)=x/(1+|x|), is one-one and onto.

Prove that f:ℝ→ℝ, f(x)=x³, is injective.

For a nonempty set X, on P(X) define ARB iff A⊂B. Is this an equivalence relation? State the interpretation of ⊂.

Find the number of onto functions from {1,2,…,n} to itself, for n≥1.

Let A={−1,0,1,2}, B={−4,−2,0,2}, f,g:A→B, with f(x)=x²−x and g(x)=2|x−1/2|−1. Are f and g equal? Justify.

On A={1,2,3}, how many relations containing (1,2),(1,3) are reflexive and symmetric but not transitive?

On A={1,2,3}, how many equivalence relations contain (1,2)?