Question

If U = Set of integers from -10 to 10 A=Set of integers from -1 to 1.

B=Set of first ten whole numbers

Prove that ( A intersection B)©=A©UB©

Hey c is complement

Answer 1

(A∩B)' = A'∪B'

Explanation:

U is the universal set

A and B are two subsets of U

let A' be the complement subset of A

and B' be the complement subset of B

U = {-10,-9,…,-1,0,1,…,9,10}

A = {-1,0,1}

B = {1,2,…,9,10}

Then

A∩B = {1}

Then

the complement of A∩B :

(A∩B)' = {-10,-9,…,-1,0,2,…,9,10}

(notice the absence of 1)

On the other hand,

A' = {-10,…,-2}∪{2,…,10}

B' = {-10,…,0}

Then

A'∪B' = {-10,-9,…,-1,0}∪{2,…,10}

= {-10,-9,…,-1,0,2,…,9,10}

Conclusion:

(A∩B)' = A'∪B'