Math worksheet with set theory exercises on intersections, unions, and number properties.

1. Given:
- A = {1, 2, 3, 4, 5, 6}
- B = {1, 2, 3}
- C = {3, 4, 5}

(a) A ∩ B = {1, 2, 3} (common elements in A and B)
(b) A ∩ C = {3, 4, 5} (common elements in A and C)
(c) B ∩ C = {3} (common elements in B and C)
(d) A ∪ B = {1, 2, 3, 4, 5, 6} (all elements in A or B)
(e) (A ∩ B) ∪ C = {1, 2, 3} ∪ {3, 4, 5} = {1, 2, 3, 4, 5}
(f) (A ∪ C) ∩ B = {1, 2, 3, 4, 5, 6} ∩ {1, 2, 3} = {1, 2, 3}

2. Given:
- X = The set of positive even numbers less than 9 = {2, 4, 6, 8}
- Y = The set of positive odd numbers less than 9 = {1, 3, 5, 7}
- Z = The set of numbers between 1 and 10 = {1, 2, 3, 4, 5, 6, 7, 8, 9}

(i) List the sets:
- X = {2, 4, 6, 8}
- Y = {1, 3, 5, 7}
- Z = {1, 2, 3, 4, 5, 6, 7, 8, 9}

(ii) Find:
- X ∩ Y = {} (no common elements between even and odd numbers)
- X ∩ Z = {2, 4, 6, 8} (common elements in X and Z)
- Y ∩ Z = {1, 3, 5, 7} (common elements in Y and Z)