Explore how sets relate to each other — subsets, unions, and intersections — and represent them with Venn diagrams.
Set A is a subset of set B if every element of A is also in B. A finite set has a countable number of elements; an infinite set does not. An empty set has no elements at all, written as { } or ∅.
If A = {1, 2} and B = {1, 2, 3, 4}, is A a subset of B?
Yes, since every element of A (1 and 2) is also in B
Is the set of all even numbers finite or infinite?
Infinite, since even numbers go on forever
The union of two sets (A ∪ B) contains all elements that are in A, in B, or in both. The intersection (A ∩ B) contains only the elements common to both sets.
If A = {1, 2, 3} and B = {3, 4, 5}, find A ∪ B.
{1, 2, 3, 4, 5}
If A = {1, 2, 3} and B = {3, 4, 5}, find A ∩ B.
{3}, the only element in both sets
1. If A = {2, 4, 6} and B = {2, 4, 6, 8, 10}, is A a subset of B?
2. Is the set of days in a week finite or infinite?
3. If A = {a, b, c} and B = {c, d, e}, find A ∪ B.
4. If A = {a, b, c} and B = {c, d, e}, find A ∩ B.
5. If P = {1, 2, 3, 4, 5} and Q = {6, 7, 8}, find P ∩ Q.