Subset - Examples

Examples

  • The set {1, 2} is a proper subset of {1, 2, 3}.
  • Any set is a subset of itself, but not a proper subset.
  • The empty set { }, denoted by ∅, is also a subset of any given set X. It is also always a proper subset of any set except itself.
  • The set {x: x is a prime number greater than 10} is a proper subset of {x: x is an odd number greater than 10}
  • The set of natural numbers is a proper subset of the set of rational numbers and the set of points in a line segment is a proper subset of the set of points in a line. These are examples in which both the part and the whole are infinite, and the part has the same number of elements as the whole; such cases can tax intuition.

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