Question

Let A = {0,2,4,6} B = {1,2,3,4,5} and C = {2,4,6,8}
Verify:- (A ∪ B ) ∪ C = A ∪ (B ∪ 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)

(ii) Using Venn diagram, we have

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

hope it is useful for you and have a sweet day and please follow

Answer 2

Given

• A = {0,2,4,6}

• B = {1,2,3,4,5}

• C = {2,4,6,8}

To Verify

• (A ∪ B) ∪ C = A ∪ (B ∪ C)

Solution

➙ We have :

→ A ∪ B =  {0,2,4,6} ∪ {1,2,3,4,5} = {0,1,2,3,4,5,6}

∴ (A ∪ B) ∪ C :

→ {0,1,2,3,4,5,6} ∪ {2,4,6,8}  = {0,1,2,3,4,5,6,8}

➙ We have :

→ B ∪ C = {1,2,3,4,5} ∪ {2,4,6,8} = {1,2,3,4,5,6,8}

∴ A ∪ (B ∪ C) = {0,2,4,6} ∪ {1,2,3,4,5,6,8} = {0,1,2,3,4,5,6,8}

➙ Hence :

→  (A ∪ B) ∪ C = A ∪ (B ∪ C)

Learn more

• Union Sets :- The union of two sets A and B, denoted by A ∪ B is the set of all those elements, each one of which is either in A or in B or in both A and B.