Lesson – Unions and Intersections
Union
In English, this word means:
In Math, this word refers to:
“What’s yours is mine and what’s
mine is yours!”
Symbol:
Intersection
In English, this word means:
In Math, I have heard this word when…
In Math, this word refers to:
Symbol:
Let’s take a look at a few examples.
Example: Let’s look at the letters that make up the word pig and guppy.
a. What are all the letters that make the word pig?
b. What are all the letters that make the word guppy?
c. What is the union of all the letters that make up pig OR guppy?
d. What is the intersection of all the letters that make up the word
pig AND guppy?
Example: List all the colors on the clothes that you are wearing right now.
Now turn to your buddy and list all the colors on the clothes THEY are
wearing right now.
a. What is the union of all the colors you OR your buddy is wearing?
b. What is the intersection of all the colors you AND your buddy is wearing?
Example: Let’s think numbers! Set A includes all the evens numbers from 1-10. Set B
includes all the whole numbers from 5-15.
a. Find Set A ⋃ Set B.
b. Find Set B ⋂ Set A.
c. Find Set A ⋂ Set B. Does the order change your answer?
Example: Set A includes all the odd numbers from 11-20. Set B includes all the even
numbers from 11-20.
a. Find Set A ⋃ Set B.
b. Find Set B ⋂ Set A.
c. What does it mean to be a disjoint set?
You try some on your own!
1. Set A = {2, 4, 6, 8, 10, 12}, set B = {3, 6, 9, 12, 15} and set C = {1, 4, 7, 10, 13,
16}.
Find:
(i) A ∪ B
(ii) A ∩ B
(iii) B ∩ A
(iv) B ∪ A
(v) B ∪ C
(vi) Is A ∪ B = B ∪ A?
(vii) Is B ∩ C = B ∪ C?
2. If A = {1, 3, 7, 9, 10}, B = {2, 5, 7, 8, 9, 10}, C = {0, 1, 3, 10}, D = {2, 4, 6, 8,
10}, E = {negative natural numbers} and F = {0}
Find:
(i) A ∪ B
(ii) E ∪ D
(iii) C ∪ F
(iv) C ∪ D
(v) B ∪ F
(vi) A ∩ B
(vii) C ∩ D
(viii) E ∩ D
(ix) C ∩ F
(x) (A ∪ B) ∩ (A ∩ B)
(xi) (A ∪ B) ∪ (A ∩ B)
3. If A = {2, 3, 4, 5}, B ={c, d, e, f} and C = {4, 5, 6, 7};
Find:
(i) A ∪ B
(ii) A ∪ C
(iii) (A ∪ B) ∩ (A ∪ C)
(iv) A ∪ (B ∩ C)
(v) Is (A ∪ B) ∩ (A ∪ C) = A ∪ (B ∩ C)?
4. State whether the following are true or false. Then explain why or why not.
(i) If A = {5, 6, 7} and B = {6, 8, 10, 12}; then A ∪ B = {5, 6, 7, 8, 10, 12}.
(ii) If P = {a, b, c} and Q = {b, c, d}; then p intersection Q = {b, c}.
(iii) Union of two sets is the set of elements which are common to both the sets.
(iv) Two disjoint sets have at least one element in common
(v) If two sets overlap, then they must have all their elements in common
(vi) If two given sets have no elements common to both the sets, the sets are said to
be disjoint.
(vii) If A and B are two disjoint sets then A ∩ B = { }, the empty set.
(viii) If M and N are two overlapping sets then intersection of two sets M and N is not
the empty set.
Challenge thinking:
Come up with Set A and Set B such that their union is the set {5, 4, 12, 9, -8, 7} but
their intersection is { }. Explain why your two sets work.
How can we visualize this?
We use a diagram called a VENN diagram:
Example: Draw a Venn diagram for our first example: “the letters that make up
the word pig and guppy.”
Example: Draw a Venn diagram of your own.
6. Find country lovers ⋃ rock lovers =
7. Find rap lovers ⋂ rock lovers =
Homework