Mathematics: Sets Relations Functions: Properties of Complement of Sets

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Properties of Complement of Sets

Properties of complement

Properties of Complement

Properties of complement

1. Complement Law’s:

2. De Morgan’s Law:

3. Law of double complementation

4. Law of empty set and universal set i.e.:

And

Intersection of Sets

It is clear, that there are some elements which are common to both the sets and. Set of these common elements is said to be intersection of and and is denoted by.

Note:

If then and are said to be disjoint sets. In Venn diagram disjoint sets can be represented as

Venn diagram disjoint sets

Venn Diagram Disjoint Sets

Venn diagram disjoint sets

Example:

Given that

and

Find (i)

(ii) Represent using Venn diagram.

Solution:

(i) As there are only four kings out of playing cards, therefore the set has only four elements. The set has elements as there are spade cards but out of these spade cards there is one king also. Therefore, there is one common element in and.

(ii)

Represent A∩B using Venn diagram

Represent a∩B Using Venn Diagram

Represent A∩B using Venn diagram

Union of Sets

Consider the following examples:

  • is a set having all players of Indian men cricket team and is a set having all players of Indian women cricket team. Clearly and are disjoint sets. Union of these two sets is a set having all players of both teams and it is denoted by.

  • is a set having all players of cricket team and is the set having all players of Hockey team, of your school. Suppose three players are common to both the teams then union of and is a set of all players of both the teams but three common players to be written once only.

Example:

Find (i)

(ii) Represent using Venn diagram.

Solution:

  1. Represent A∪B using Venn diagram

    Represent a∪B Using Venn Diagram

    Represent A∪B using Venn diagram

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