Question

4.If A= {2,4,5,6) B = {4,5 } and C={1,2,3,7), then verify that
i) AUB = BUA ii) (AUB)UC = AU(BUC).​

Answer 1

Step-by-step explanation:

i) A U B = {2,4,5,6}

BUA = {2,4,5,6}

thus

AUB = BUA

ii) (AUB) U C = {1,2,3,4,5,6,7}

A U (BUC) = {1,2,3,4,5,6,7}

thus

(AUB)UC = AU(BUC)

Answer 2

Answer:

Step-by-step explanation:

Given,

A = {2,4,5,6},B={4,5}and C={1,2,3,7}

(1 ) A∪B = B∪A

A∪B = {2,4,5,6}∪{4,5} = {2,4,5,6}

B∪A = {4,5} ∪{2,4,5,6} = {2,4,5,6}

∴ A∪B = B∪A is proved.

( 2 ) ( A ∪B) ∪ C = A ∪ ( B ∪ C )

( A ∪ B) ∪C = {2,4,5,6} ∪{1,2,3,7} = {1,2,3,4,5,6,7} [∵A∪B={2,4,5,6} ]

( B ∪C) = { 4,5}∪{1.,2,3,7} = {1,2,3,4,5,7}

A ∪ ( B ∪C ) = {2,4,5,6} ∪{1,2,3,4,5,7} = { 1,2,3,4,5,6,7} [∵B ∪ C={1,2,3,4,5,7} ]

∴ (A ∪ B) ∪C = A ∪(B ∪C) is proved.