Subsets
Maths: Edexcel A Level Pure Maths, topic 1.2.2
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.
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.
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.
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
Test yourself on Subsets
Which of the following relations is true?
A = {3,5,6} and B = {1,2,3,4,5,7,8,9}Which of the following relations is true?
A = {2, 6} and B = {Even numbers}Which of the following relations is true?
A = {Square numbers} and B = {All positive numbers}