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Write any three non-empty and overlapping sets A , B , and C. Then verify the following:
1.A U (B intersection C)= (A U B) intersection (A U c)
2.A U (B U C)= (A intersection B) U (A intersection C)
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Let A,B,C be any sets.
If we take intersection of sets, it should be distributive over union of sets.
Let's take union of B and C i.e. B∪C and then intersect with A.
∴ Finally we get A∩(B∪C), which is same as union of intersection of A,B and A,C.
i.e. A∩(B∪C)=(A∩B)∪(A∩C)
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