Question

A={4,5,6,7},B={8,9}C={10}
find A×(B-C)=(A×C)-(A×C)
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Answer 1

Step-by-step explanation:

ANSWER

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

For the LHS:

Union of two sets will have the elements of both sets.

So, B∪C={2,3,4,5,6,8}

A−(B∪C) will have elements of A which are not in (B∪C)

So, A−(B∪C)={1} ..... (1)

For the RHS:

A−B will have elements of A which are not in B.

So, A−B={1,3,5}

A−C will have elements of A which are not in C.

So, A−C={1,2}

Intersection of two sets has the common elements of both the sets.

⇒(A−B)∩(A−C)={1} ..... (2)

From (1) and (2), we have

A−(B∪C)=(A−B)∩(A−C)

Hence, the given expression is true.