Definitions
An unordered collection of distinct objects called elements or members.
Set
A rule that assigns each input exactly one output.
Function
Let A = {x | x is a positive even number ≤ 6}.
Write A using roster notation.
A = {2, 4, 6}
True/False.
A = {1, 2, 3} is a subset of B = {1, 2, 3, 4}
True
How do you denote the number of elements in a set A?
|A|
What is the symbol for the empty set?
∅ or {}
A type of sequence where each term is decreased by a common difference.
Arithmetic Sequence
Given A = {4,5,6,2,5,2} and B = {8,4,2,5,6,1}, find A ∪ B.
A ∪ B = {1,2,4,5,6,8}
Let U = {1, 2, 3, 4, 5, 6}, A = {2, 4, 6}.
What is the complement of A?
A̅ = {1,3,5}
What is the formula for the cardinality of the union of two sets A and B?
|A ∪ B| = |A| + |B| - |A ∩ B|
The set of all subsets of a given set.
Power Set
Find the 5th term of the geometric sequence: 2, 4, 8, ...
32
Given A = {1, 2, 3}, how many subsets does A have?
8 subsets
Given:
A = {1,5,8,3,4,2,7,9}
B = {5,4,2,7,4,0,2}
Find: A−B
A−B = {1,3,8,9}
In a survey of 100 students:
60 like football
45 like basketball
25 like both
a. How many students like only football?
b. How many like only basketball?
c. How many like either but not both?
a. 35
b. 20
c. 55
What is the difference between the roster method and the rule method?
Roster method lists all elements, while rule method describes properties that define the set.
BONUS QUESTION!
+400 points
Given:
U = {0, 1, 2, 3, 4, 5, 6}
A = {0, 2, 4}
B = {2, 3, 5}
Find the complement of A∪B
Complement of A∪B = {1,6}
Let U = {1–10}, A = {2, 4, 6, 8}, B = {3, 6, 9}.
Compute: (A−B) ∩ B
(A−B) ∩ B = ∅ or {}
In a group of 120 students, 60 like dogs, 70 like cats, and 40 like both. How many like either cats or dogs but not both?
50
What is the constant multiplied in geometric sequences?
Common Ratio
Find the linear relationship of the given data points.
x y
1 2
3 6
4 8
5 10
Y=2x
Given:
A = {0,1,2,3,4,5}
C = {0,2,4,6,8,10}
Find: A△C
A△C = {1,3,5,6,8,10}
Let:
U={0,1,2,3,4,5,6,7,8,9,10}
A={1,2,3,4,5}
B={4,5,6,7}
C={2,4,6,8}
Find (A−C) ∪ (B∩C).
(A−C) ∪ (B∩C) = {1,3,4,5,6}
In a survey of 100 first-year BSIT students, it was found that:
55 students use Facebook (F)
40 students use Instagram (I)
60 students use TikTok (T)
25 students use both Facebook and Instagram
30 students use both Instagram and TikTok
35 students use both Facebook and TikTok
15 students use all three platforms
a. How many students use only Facebook?
b. How many students use none of the three?
c. How many students use exactly two of the platforms?
a. 10
b. 20
c. 45