Relations and Functions Class 12 Maths Notes – Formulas & Quick Revision

Class 12 Relations and Functions mein equivalence relations, one-one/onto functions aur composition aate hain. Yahan aapko is chapter ke sabse important formulas aur quick revision points free milte hain — NCERT/CBSE syllabus ke hisaab se, boards aur JEE/NEET dono ke liye.

Important Formulas & Concepts — Relations and Functions

• Reflexive: (a,a) ∈ R ∀ a
• Symmetric: (a,b) ∈ R ⟹ (b,a) ∈ R
• Transitive: (a,b),(b,c) ∈ R ⟹ (a,c) ∈ R
• Equivalence = reflexive + symmetric + transitive
• One-one (injective): f(x₁) = f(x₂) ⟹ x₁ = x₂
• Onto (surjective): range = codomain
• Bijective = one-one + onto (invertible)
• (gof)(x) = g(f(x))

Quick Revision Points

• Equivalence relation check karna 6-marker classic hai
• One-one check: horizontal line test ya derivative ka sign
• Number of functions A→B = nᵐ; one-one = nPm
• f invertible ⟺ bijective
• gof ≠ fog generally

FAQ

Equivalence relation ke questions kaise likhu?

Teeno properties alag-alag prove karo — PDF mein model answer format diya hai.

One-one/onto proof mein galti hoti hai?

PDF ka step-wise method follow karo — assume, solve, conclude.

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