## Laws on set operations

Some Laws on set operations are discussed here:

• 1. Identity laws:

A∪∅=A

A∩U=U

• 2. Domination laws:

A∪U=U

A∩∅=∅

• 3. Idempotent laws:

A∪A=A

A∩A=A

• 4. Commutative laws:

A∪B=B∪A

A∩B=B∩A

Example:

• For the following sets verify both commutative laws. The sets are A={1,2,3,7,8} and B={2,3,4,5,9}.

• Solution:

First let us commutative law for the operation union.

A={1,2,3,7,8}

B={2,3,4,5,9}.

A∪B={1,2,3,7,8,4,5,9}={1,2,3,4,5,7,8,9}

B∩A={2,3,4,5,9,1,7,8}={1,2,3,4,57,8,9}

So,A∪B=B∩A.

• Now let us verify for intersection:

• A∩B={2,3}

B∩A={2,3}

so, A∩B={2,3}=B∩A

So both the commutative laws are verified.

Related Topics

• Set theory
• Representation of Set
• types of set
• Disjoint sets
• Power Set
• Operations on Sets
• Laws on set operations
• More Laws
• Venn diagrams
• Set word problems
• Relations and functions
• # Quote on Mathematics

“Mathematics, without this we can do nothing in our life. Each and everything around us is math.

Math is not only solving problems and finding solutions and it is also doing many things in our day to day life. They are: