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:

    It subtracts sadness and adds happiness in our life.

    It divides sorrow and multiplies forgiveness and love.

    Some people would not be able accept that the subject Math is easy to understand. That is because; they are unable to realize how the life is complicated. The problems in the subject Math are easier to solve than the problems in our real life. When we people are able to solve all the problems in the complicated life, why can we not solve the simple math problems?

    Many people think that the subject math is always complicated and it exists to make things from simple to complicate. But the real existence of the subject math is to make things from complicate to simple.” Previous page     Next page

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