Sets

1. Subsets and Supersets

Consider two given sets A and B. If the set A consists of some or all elements of the

set B, then A is said to be a subset of B. We denote this by set notation ⊆. Thus A ⊆ B

means; A is a subset of B. if the set A is a subset of B with at least an element in B

not in A, then the set A is called a proper subset of B. Thus A ⊂ B means, A is a proper

subset of B. B is considered a superset of A.

The set notation for superset is ⊃. Thus B ⊃ A means B is a superset of A.

Example

If P = {2, 4, 6, 8,10}, Q = {4, 10}, R = {6, 8} and S = {2, 4, 6, 8, 10, 12}, then:

Q ⊂ P (ii) R ⊂ P (iii) S ⊃ P

In sets, the order in which the elements are written is irrelevant. For instance, {2, 4, 6,8} is the same as {2, 6, 8, 4}.