Sets and operations on them
Answers are for parents and teachers.
1
Write the elements of {x | −3 < x ≤ 2, x ∈ Z} and find n.
{−2, −1, 0, 1, 2}; n = 5
2
U = {1, 2, …, 15}, A = the multiples of 3, B = {x | x ≤ 7, x ∈ N}. Find A ∩ B′.
A = {3, 6, 9, 12, 15}, B′ = {8, …, 15}; A ∩ B′ = {9, 12, 15}
3
n(U) = 60, n(A) = 32, n(B) = 25, n(A ∩ B) = 10. How many elements lie in neither set?
13
4
Write all subsets of {p, q}.
∅, {p}, {q}, {p, q}
5
Explain with an example why A ∩ B ⊆ A ∪ B always holds.
A common element lies in both sets, so it lies in at least one. For example {1, 2} ∩ {2, 3} = {2} ⊆ {1, 2, 3}.