Sets, Relations and Functions Class 11 Notes with Examples

Sets, Relations and Functions form the base of Class 11 and 12 Maths. The chapter is scoring — most questions are direct formula or definition applications.

Sets

• Roster {1, 2, 3} vs set-builder {x : x ∈ N, x < 4}
• Subsets: a set with n elements has 2ⁿ subsets, 2ⁿ − 1 proper subsets
• Power set P(A); universal set U; complement A′
• Operations: A ∪ B, A ∩ B, A − B, A Δ B
• n(A ∪ B) = n(A) + n(B) − n(A ∩ B); for three sets add n(A ∩ B ∩ C) and subtract the three pair intersections

Example

In a class of 60, 35 like tea, 30 like coffee, 15 like both. Only tea = 20, only coffee = 15, neither = 60 − 50 = 10.

Relations

• Cartesian product A × B; n(A × B) = n(A) n(B)
• A relation is any subset of A × B; number of relations = 2^(mn)
• Domain = set of first elements; range = set of second elements
• Types (Class 12): reflexive, symmetric, transitive, equivalence

Functions

• Every element of the domain maps to exactly one image
• One-one (injective): different inputs, different outputs; onto (surjective): range = codomain
• Domain of √(x − 2): x ≥ 2; domain of 1/(x² − 4): x ≠ ±2
• Range of f(x) = x² + 1 is [1, ∞)
• Graphs to know: identity, constant, modulus, signum, greatest integer

Common mistakes

• Forgetting the empty set is a subset of every set
• Writing range as the codomain
• Missing values that make the denominator zero

Related: Trigonometry identities.

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Frequently asked questions

Are these Sets, Relations and Functions Class 11 Notes with Examples notes enough for the exam?

They cover every formula, definition and question type that appears in school and board papers for this chapter. Use them with the NCERT examples, exercise questions and the last five years' papers to be fully prepared.

How should I revise Sets, Relations and Functions Class 11 Notes with Examples?

Revise the notes after 1 day, 7 days and 30 days. Solve five questions each time instead of only reading, and keep an error list of the steps you get wrong.

What if I get stuck on a sets class 11 question?

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