Question

Answer the following question If A = { a, c, e, f, h }, B = { c, d, e, f } and C = { a, b, c, f } then verify that n ( AUBUC ) = n ( A ) + n ( B) + n ( C ) - n ( A intersection B) - n ( B intersection C ) - n ( A intersection C ) + n ( A intersection B intersection C )

Answer 1

Answer:

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.

Answer 2

Step-by-step explanation:

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