More types of sets: Disjoint sets, Subset and Universal set

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Disjoint sets:

Two or more sets are said to be disjoint if they have no common elements.

Disjoint-sets are also known as non overlapping sets.

For example:

A={2,4,6,8} and B={1,3,5,7}. Here A and B have no common element. So A and B are disjoint-sets.

Overlapping-sets:

Two-sets are said to be overlapping-sets if they contain at least one element in common.

For example:

A={2,4,6,8}

B={3,6,9}here A and B have one common element that is 6. So A and B are overlapping sets.

Universal set:

A universal set is a set of all possible elements under given definition. It is usually denoted by U or ξ .

Subset:

If A and B are two given sets, and if all the elements of A are also elements of B, then A is a subset of B.

If all elements of set B are also element of A then B is a subset of A.

In other words, A is a subset of B if and only if every element of A is in B

The symbol to denote subset is ⊆.

For example, If A is a subset of B, then it is denoted by A⊆B.

Type of subset:

Proper subset:

A is a proper subset of B if and only if every element of A must also be the element of the set B, and also there exists at least one element in B which is not an element of A

Note:

The symbol to denote proper subset is ⊂ .

Every set is a subset of itself. A⊂ A.

Empty set or null set or ∅ is the subset of every set

When we say that A is a subset of B we denote by A⊆B.

When we say that A is a proper subset of B then we denote it as A⊂B.

Super set:

Whenever A is a subset of B, then B is the super set of A. It is expressed as B⊇A.

Examples:

U={x:x is a natural number; 1‹x‹10}

A={x:x is a even natural number; x‹10}

B={x:x∈N;x=3N;x≤9}

C={2,4,6}

The sets can be written in Roster form as

U={2,3,4,5,6,7,8,9}

A={2,4,6,8}

B={3,6,9}

C={2,4,6}

So, let us write the subsets and super sets here:

A⊂U, that is A is a proper subset of the universal set U.

B⊂U, that is B is a proper subset of U

C⊂A, that is C is a proper subset of A

A⊇C, that is A is super set of C.

These are the types of sets other than disjoint sets.
Related Topics

We had seen disjoint sets, overlapping sets, universal sets and subsets in this page 'Disjoint sets'. If you are having any doubt you can contact us through mail, we will help you to clear your doubts.