Question

Let A={0,2,4,6},B={1,2,3,4,5}and C={2,4,6,8}.
Verify that :(AUB)UC=AU(BUC).

Answer 1

(U → UNION): All elements in both the sets
(Π → INTERSECTION): common elements from both the sets

A={0,2,4,6},
B={1,2,3,4,5}, and
C={2,4,6,8}

AUB = {0,1,2,3,4,5,6}
Now, (AUB)UC = {0,1,2,3,4,5,6,8}

BUC = {1,2,3,4,5,6,8}
AU(BUC) = {0,1,2,3,4,5,6,8}
Now, (AUB)UC = AU(BUC)

Since, LHS = RHS
Hence proved.

(if you still have any doubt, ask in the comment)
Thankyou!!!

Answer 2

Answer:

given:

A = 0,2,4,6

B=1,2,3,4,5

C=2,4,6,8

L.H.S = (AUB)UC

(AUB)=(0,2,4,6)U(1,2,3,4,5)

= (0,1,2,3,4,5,6)

(AUB)UC = (0,1,2,3,,4,5,6)U (2,4,6,8)

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

R.H.SV= AU(BUC)

BUC = (1,2,3,4,5)U(2,4,6,8)

= {1,2,3,4,5,6,8}

AU(BUC) = (0,2,4,6)U ( 1,2,3,4,5,6,8)

{0,1,2,3,4,5,6,8}.....

L.H.S=R.H.S..

H/P

Step-by-step explanation:

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