Question

Let A - {0,1,2,3,4,5}, B = {1, 2, 4, 6, 8} and c={1,3,5,7)
Verify (A intersection B) intersection C= A intersection (B intersection C)​

Answer 1

Answer:

First, we find A∪(B∩C)

Consider B∩C= {1, 2, 3, 4, 5 ,6} ∩ {2, 4, 6, 7} = {4,6}

A∪(B∩C) = {0,1,2,3,4} U = {4, 6} , = { 0, 1, 2, 3, 4, 6}. (1)

Next, consider A∪B = {0,1, 2, 3, 4} ∪ {1, -2, 3, 4, 5, 6}

= { -2, 0, 1, 2, 3, 4, 5, 6},

A∪C, = {0, 1, 2, 3, 4} ∪ {2, 4, 6, 7} = {0, 1, 2, 3, 4, 6, 7}.

Thus, (A∪B)∩(A∪C) = {-2, 0, 1, 2, 3, 4, 5, 6} ∩ {0, 1, 2, 3, 4, 6, 7}

= {0, 1, 2, 3, 4, 6}. (2)

From (1) and (2), we get A∪(B∩C)=(A∪B)∩(A∪C)

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