Intersection and Union Sample Problems

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Here are some tips for Intersection and Union, which aligns with New York state standards:

Intersection and Union

A set is a defined collection of members or elements.

C = { A, -3, H, 5, 4, C }
Set C contains 6 members or elements: A, -3, H, 5, 4, and C.
D = {} E = ∅
If a set has no members, it is an empty set. Sets D and E are both empty sets.

The intersection of two sets A and B, written as A ∩ B, is the set of all members common to both A and B.

The dark shaded region represents A ∩ B.

The union of two sets A and B, written as A ∪ B, is the set of all members in A and all members in B.

The dark shaded regions represents A ∪ B.

An easy way to remember: Union is ∪

Example 1

Write answers in ascending order, separated by commas. Example: A = {-3, 1, 2, 5 }.
G = { 0, 3, 5 } H = { 2, 3, 4, 5 }

Intersection Union

G 0 3 5

H 2 3 4 5

↓ ↓

G ∩ H 3 5

G 0 3 5

H 2 3 4 5

↓ ↓ ↓ ↓ ↓

G ∪ H 0 2 3 4 5

G ∩ H = {} G ∪ H = {}

Example 2

Write answers in ascending order, separated by commas. Example: A = {-3, 1, 2, 5 }.
G = { -2, -1, 0, 4, 5 } H is the set of positive even numbers.
Find G ∩ H.
H contains any and all positive even numbers.
So an intersection of sets G and H is the set of positive even numbers in set G.
Remember that 0 is neither positive or negative.

G -2 -1 0 4 5

positive ✓ ✓

even ✓ ✓ ✓

↓

G ∩ H 4

G ∩ H = {}