Question

if μ=[2,3,4,5]A=[2,4]and B=[3,4] then verify that 1.A-B=A∩B 2.[A∪B]1=A1∩B1

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.