Question

Let U={1,2,3,4,5,6,7},A={1,3,5,7} and B={0,2,3,5,7},find the following sets. 1.A' 2.B' 3.A'intersectionB' 4.A'unionB' 5. (A union B)' 6.(A intersection B)' 7.(A')' 8.(B')'

Answer 1

If u={1,2,3,4,5,6,7}
A={1,3,5,7}
B={0,2,3,5,7}
A'={0,2,4,6}
B'={1,4,6}
A' interaction B'={4,6}
A' union B'={0,1,2,4,6}
(A union B )'={4,6}
(A interection B)'={0,1,2,4,6}
(A')'={1,3,5,7}=A
(B')'={0,2,3,5,7}=B

Answer 2

1. A' = {2, 4, 6}

i.e., the elements that are not present in A but present in U.

2. B' = {1, 4, 6}

i.e., the elements that are not present in B but present in U.

3. A' intersection B' = {4, 6}

i.e., the elements common to both A' and B'.

4. A' union B' = {0, 1, 2, 3, 5, 7}

Union denotes the whole of elements present in both the sets.

5. A union B = {0, 1, 2, 3, 5, 7}

(A union B)' = {4, 6}

6. A intersection B = {3, 5, 7}

(A intersection B)' =  {0, 1, 2, 3, 5, 7}

7. (A')' = A = {1,3,5,7}

8. (B')' = B = {0,2,3,5,7}

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