Question

If U={a, b, c, d, e, f, g, h}, A={b, d, f, h} and B={a, d, e, h}, find the following sets.
A'∪B' =

Answer 1

Answer:

AUB is the set of elements which are in A or B or in both

AnB is the set of all elements common to both A and B

A' is the set of all elements which are not in A

B' is the set of all elements which are not in B

U={a, b, c, d, e, f, g, h}

A={b, d, f, h} and B={a, d, e, h}

1. A' ={a, c, e, g}

2. B' ={b, c, f, g}

3. A'UB'= { a, b, c, e, f, g}

4. A' n B' = { c, g}

5. AUB = {a, b,d, e, f, h}

(AUB)' = {c, g}

6. AnB= {d, h}

(AnB)' = {a, b, c, e, f, g}

7. (A')' = {b, d, f, h}

8. (B')' = {a, d, e, h}

Answer 2

A' ∪ B' = { a , b , c , e , f , g }

Given :

U = {a, b, c, d, e, f, g, h} , A = {b, d, f, h} and B = {a, d, e, h}

To find :

The set A' ∪ B'

Solution :

Step 1 of 2 :

Find A' and B'

Here it is given that

U = {a, b, c, d, e, f, g, h}

A = {b, d, f, h}

B = {a, d, e, h}

Thus we get

A'

= { x ∈ U : x ∉ A }

= {a, c, e, g}

B'

= { x ∈ U : x ∉ B }

= {b, c, f, g}

Step 2 of 2 :

Find the set A' ∪ B'

A' ∪ B'

= { x : x ∈ A' ∨ x ∈ B' }

= { a , b , c , e , f , g }

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