Sets, Relations and Functions: One-Page Formula Sheet

Sets, Relations and Functions — formula sheet

Formulas

• n(A ∪ B) = n(A) + n(B) − n(A ∩ B)
• Number of relations on a set with n elements = 2^(n²)
• Number of functions from A (m) to B (n) = nᵐ
• One-one functions = ⁿPₘ (n ≥ m)

Key ideas

• Equivalence relation = reflexive + symmetric + transitive
• A function has an inverse only if it is one-one and onto
• Domain first: denominators ≠ 0, even roots ≥ 0, log arguments > 0
• fog(x) means f(g(x))

Traps to avoid

• Skipping a domain condition
• Assuming every relation is a function
• Order of composition

jeevisionary.in/jee-topics/maths/sets-relations-functions/