Question:

Find A union B. Find A intersection B. Draw the Venn diagram.

Solution:

1. (a) Let A = {1,3,5,7,9} and B = {1,4,7,8,9,10} be subsets of the universal set
ξ = {x ∈ Z:1 ≤ x ≤ 10}

1. Find A ∩ B .

   A ∩ B = {1,3,5,7,9} ∩ {1,4,7,8,9,10}
   = {1,7,9}

2. Find A ∪ B .

   A ∪ B = {1,3,5,7,9} ∪ {1,4,7,8,9,10}
   = {1,3,5,7,9,4,8,10}

3. Find A - B .

   A - B = {1,3,5,7,9} - {1,4,7,8,9,10}
   = {3,5}

4. Find A'

   A ' = ξ -A
   = {1,2,3,4,5,6,7,8,9,10} - {1,3,5,7,9}
   = {2,4,6,8,10}

2. (b) Let X Y Z , , and be sets. 

Draw the Venn diagram of   (X ∪ Y ) ∩ Z'.

 

Draw the Venn diagram of   X ∪ (Y  ∩ Z').

From the above Venn diagrams.
(X ∪ Y ) ∩ Z' = X ∪ (Y  ∩ Z')