Question

If A and B are any two sets, then prove that AUB=(A-B)U(B-A)U(A∩B) ​

Answer 1

Answer:

let,

    set A={1,3,5,7,9}

    set B={2,4,6,8,10}

according to the question

 AUB=(A-B)U(B-A)U(A∩B)

so taking L.H.S.=AUB

        AUB={1,3,5,7,9}U{2,4,6,8,10}={1,2,3,4,5,6,7,8,9,10}

∴AUB=L.H.S.={1,2,3,4,5,6,7,8,9,10}

now,

   taking R.H.S=(A-B)U(B-A)U(A∩B)

A-B={1,2,3,5,9} - {2,4,6,8,10} ={1,3,5,7,9}  

∴A-B={1,3,5,7,9}  

B-A= {2,4,6,8,10} - {1,2,3,5,9} =  {2,4,6,8,10}

∴B-A= {2,4,6,8,10}

A∩B= {1,2,3,5,9}  ∩ {2,4,6,8,10} = {}

∴A∩B = {}

so,

  R.H.S.= (A-B)U(B-A)U(A∩B)={1,3,5,7,9} U {2,4,6,8,10} U {}

            ={1,2,3,4,5,6,7,8,9,10}

Since,  AUB=(A-B)U(B-A)U(A∩B)

∴  AUB=(A-B)U(B-A)U(A∩B)proved

         

you can use any number or alphabets in the set A and B.

Step-by-step explanation: