1.2.2

Subsets

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Subsets

As we have seen previously, the universal set contains all elements, and can also contain sets. We say that these sets are subsets of the universal set.

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Subsets

  • Subsets are sets contained within other sets.
  • The set A is a subset of set B if all of the elements in A are also elements in B.
  • For example the set A = {2, 3, 4} has the following subsets:
    • {2, 3}, {3, 4}, {2, 4}, {2}, {3}, {4}, {2,3,4}
  • Every set is its own subset.
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Proper subsets

  • Proper subsets of the set A are all the subsets that do not equal A.
  • For example, the set A = {2, 3, 4} has the following proper subsets:
    • {2, 3}, {3, 4}, {2, 4}, {2}, {3}, {4}
  • {2, 3, 4} is not a proper subset of A.
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Notation

  • If A is a subset of B, we write:
    • A ⊆ B
  • If A is a propersubset of B, we write:
    • A ⊂ B
  • If C is not a subset of B, we write:
    • C ⊄ B

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1Proof

2Algebra & Functions

2.1Powers & Roots

2.2Quadratic Equations

2.3Inequalities

2.4Polynomials

2.5Graphs

2.6Functions

2.7Transformation of Graphs

2.8Partial Fractions (A2 Only)

3Coordinate Geometry

4Sequences & Series

5Trigonometry

6Exponentials & Logarithms

7Differentiation

8Integration

9Numerical Methods

10Vectors

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