Intersection and Union

Consider a set A and a set B. Union of set A and set B can be defined as a set C such that every element of C is in A or B.

Similarly, the intersection of set A and set B can be defined as a set C such that every elements of set C is in set A and set B.

For example, let A={1,3,5,7,9} and B={2,4,6,8,10}. Now, the union of set A and set B i.e. A∪B={1,2,3,4,5,6,7,8,9,10}.

Similarly, let A={1,2,3,4,5} and B={3,4,5,6,7}. Now, the intersection of set A and set B i.e. A∩B={3,4,5}.

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Let us do  another examples.

Construct a counter example for the following: For any sets A, B, C, A∩(B∪C)=(A∩B)∪C.

As we know a union is a set whose every element is in A or B and intersection is a set whose every element is in A and B. Let A={1,3,5,7,9}, B={2,3,4,5,6,8,10} and C={1,2,3,4,5}. So, B∪C={1,2,3,4,5,6,8,10}. Now, A∩(B∪C)={1,3,5}. Similarly, A∩B={3,5}. Now, (A∩B)∪C={1,2,3,4,5}. So, we conclude that A∩(B∪C)≠(A∩B)∪C.

 

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