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3.2 Subset, Universal Set and the Complement of a Set

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3.2a Subsets
1. If every element of a set A is also an element of a set B, then set A is called subset of set B.

2. The symbol ⊂ is used to denote ‘is a subset of’.
Therefore, set A is a subset of set B. In set notation, it is written as A ⊂ B.

Example:
A = {11, 12, 13} and B = {10, 11, 12, 13, 14}
Every element of set A is an element of set B.
Therefore  A ⊂ B .

3.   A ⊂ B .  can be illustrated using Venn diagram as below:


4. The symbol   ⊄ is used to denote ‘is not a subset of’.

5. An empty set is a subset of any set.
For example, ∅ ⊂ A

6. A set is a subset of itself.
For example,   B ⊂ B  

7. The number of subsets for a set with n elements is 2n.
For example, if A = {3, 7}
So n = 2, then number of subsets of set A = 22 = 4
All the subsets of set A are { }, {3}, {7} and {3, 7}.