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Cheat sheet · JEE Preparation Mathematics

Sets cheat sheet

The whole chapter on one page: key formulas, facts and the points to remember, for quick revision before a test.

JEE · Mathematics

Cheat sheet

Class 11 · Chapter 1Sets

De Morgan: complement of a union is the intersection of complements (and vice versa).

1. Basics

  • Roster form {1, 2, 3} and set-builder form {x : x is a natural number < 4}.
  • Empty set ∅, finite, infinite, equal sets.
  • Subset A⊆BA \subseteq B; power set P(A)P(A) has 2n2^n elements.
  • Intervals: (a,b)(a, b) open, [a,b][a, b] closed.

2. Operations

A∪BA\cup BA∩BA\cap BA−BA - BA′=U−AA' = U - A

Laws

  • Commutative, associative, distributive laws.
  • De Morgan: (A∪B)′=A′∩B′(A\cup B)' = A'\cap B', (A∩B)′=A′∪B′(A\cap B)' = A'\cup B'.

3. Counting

n(A∪B)=n(A)+n(B)−n(A∩B)n(A\cup B) = n(A) + n(B) - n(A\cap B)
n(A∪B∪C)=∑n(A)−∑n(A∩B)+n(A∩B∩C)n(A\cup B\cup C) = \sum n(A) - \sum n(A\cap B) + n(A\cap B\cap C)

In a class of 40, 25 like tea, 20 like coffee, 10 like both ⇒ 25 + 20 − 10 = 35 like at least one.

4. Key Points

  • ∅ is a subset of every set.
  • A − B ≠ B − A in general.
  • Disjoint sets: A ∩ B = ∅.
  • Venn diagrams show relations between sets.

Remember: Set forms | union, intersection, complement | n(A ∪ B)

Sets: questions and notes

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