Question

How can I prove that for any sets A and B, A = (A − B) ∪ (A ∩ B)?

Answer 1

Answer:

Step-by-step explanation:

Since we can write A-B = A ∩ B’

So. A = (A − B) ∪ (A ∩ B)

A = (A ∩ B’) ∪ (A ∩ B)

A = A ∩ (B∪B’)

A =A ∩ U

A= A

Answer 2

Here is the solution.....

let A = {1,3,5,7,8}

let B = {1,6,4,3,6}

now..starting form RHS side

(A-B) U (A Π B)

( { 5,7,8}) U ({1,3})

{1,3,5,7,8}

which is equal to LHS

hence proved