Question

Q7. Let A ={0,1,2,3},B ={3,4,6} and c={0,1,3}.
verify that

(i)AU(BUC)=(AUB)UC

(ii)A∩(B∩C)=(A∩B) ∩C​

Answer 1

Answer:

Step-by-step explanation:

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).