Question

2. Of A = {0, 1,2,3,4,5} and B = {0,3,5, 7}, then verify A


intersection B
=B.



​

Answer 1

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)

(ii) Using Venn diagram, we have

From (2) and (5) it is verified that A∪(B∩C)=(A∪B)∩(A∪C).

Hope it helped you..........