MATH 102
Intro to 2.2 – Subsets – Day 2
Mathematician:
Notes 09.01.16
Remember
A set is a collection of objects, which are called elements or members of the set.
If all the elements of set A are also elements of set B, then set A is a subset of set B.
Subsets use:
 or 
If all the elements of set A are also elements of set B and A  B, then set A is a proper subset of set B.
Proper Subsets use:
 since they cannot be equal to each other
Proper Subsets should be SMALLER than the original set B.
Determine if the following statements are true or false.
A) {1, 2, 3}

{1, 2, 3, 4}
B)
{X, Y, Z}

{W, X, Y, Z}
C) {a, b, c, d}

{d, a, c, b}
D)
{1, 2, 3}

{1, 2, 3, 4}
E) {X, Y, Z}

{A, B, C, D}
F)
{Illinois}

{Illinois, Indiana, Iowa}
Now consider the concept of null and empty set. What were the two symbols we used?
Determine if the following statements are true or false.
A) 12 = {
}
C)  = {  }
}={  }
B)
{
D)
{0} ={  }
Since we hopefully understand whether one set is a subset of another at this point, I would also like to
discuss how many possible subsets will occur for a given set.
Example 1:
Ms. Gajda is playing her favorite board game, SCRABBLE, and she wants to figure out how many
possible combinations of sets she can make with the letters {L, O, V, E}.
A) List all the distinct subsets for the set {L, O, V, E}.
B) Determine the number of distinct subsets for the set {L, O, V, E}.
C) How many of the distinct subsets are proper subsets?
NUMBER OF DISTINCT SUBSETS:
n=
NUMBER OF DISTINCT PROPER SUBSETS:
Tricky:
No matter what the set is,
is always a subset.
Example 2:
Nyja is ordering pizza and can add any of the following veggie topping: mushroom, onion, green
peppers. How many different variations of the pizza can Nyja make?
Believe it or not, most of the stuff from this section has been pretty concrete……………….UNTIL NOW! 
Here are some rather abstract problems to consider.
1) If A  B and B  C , must A  C ?
2) If A  B and B  C , must A  C ?
3) If A  B and B  C , must A  C ?
4) How many elements must a set have if the number of proper subsets of the set is
number of subsets of the set?
1
of the total
2
In the following exercises, if the statement is true for all sets A and U, write “true”. If it is
not true for all sets A and U, write “false”.
Assume that A   , U   and A  U .
5)
A A
6)
A A
7)
A
8)
A
9)
A U
10)

11)
 U
12)
