A, B and C are any three sets, prove that A∪(B∩C)=(A∪B)∩(A∪C)

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Q. A, B and C are any three sets, prove that
 A∪(B∩C)=(A∪B)∩(A∪C)

Solution:
Let us assume that
A={1,2,3,4,5}
B={3,5,7,9,10}
C={2,4,6,8,10}
Now,
B∩C={10}
A∪(B∩C)={1,2,3,4,5,10}=LHS
And,
A∪B={1,2,3,4,5,7,9,10}
A∪C={1,2,3,4,5,6,8,10}
(A∪B)∩(A∪C)={1,2,3,4,5,10}=RHS
Therefore LHS=RHS( hence proved)

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