2.2 Subsets.notebook
August 31, 2015
2.2 ­ Subsets
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2.2 Subsets.notebook
August 31, 2015
KEY CONCEPTS
Set A is a subset of set B, symbolized by A ⊆B, iff all of the elements of
set A are also elements of set B.
Set A is a proper subset of set B, symbolized by A ⊂B, iff all the
elements of set A are elements of set B and set A ≠ set B (that
is, set B must contain at least one element not in set A)
The number of distinct subsets of a finite set A is 2n, where n is the number of elements in set A.
The null set is always a subset of every set.
Every set is a subset of itself.
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2.2 Subsets.notebook
August 31, 2015
Example 1: Determine if set A is a subset of set B
a)A = {blue jay, robin, cardinal}
B = {blue jay, robin, chickadee, cardinal}
b)A = {2, 3, 4, 5}
B = {2, 3}
c) A = { x | x is a yellow fruit}
B = { x | x is a red fruit}
d)A = {cassette, compact disk, videotape}
B = { compact disc, videotape, cassette}
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2.2 Subsets.notebook
August 31, 2015
Example 2: Determine if set A is a proper subset of set B
a)A = {refrigerator, microwave, dishwasher}
B = {stove, refrigerator, microwave, dishwasher, garbage disposal}
b)A = {a, b, c, d}
B = {a, c, b, d}
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2.2 Subsets.notebook
August 31, 2015
Example 3: Determine whether the following are true or false
a) 3 ∈ {3, 4, 5}
b) {3} ∈ {3, 4, 5}
c) {3} ∈ {{3}, {4}, {5}}
d) {3} ⊆ {3, 4, 5}
e) 3 ⊆ {3, 4, 5}
f) { } ⊆ {3, 4, 5}
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2.2 Subsets.notebook
August 31, 2015
Example 4: Distinct Subsets
a) Determine the number of distinct subsets for the set {S, L, E, D}
b) List all the distinct subsets for the set {S, L, E, D}
c) How many of the distinct subsets are proper subsets?
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2.2 Subsets.notebook
August 31, 2015
Example 5: Variations of Ice Cream
Shanna Ruben is going to purchase ice cream at Friendly's Restaurant. To her ice cream she can add any of the following toppings: hot fudge, whipped cream, cherries, butterscotch topping, caramel topping, chopped nuts, Reese's Pieces, M & M's, Gummy Bears. How many different variations of the ice cream and toppings can be made?
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2.2 Subsets.notebook
August 31, 2015
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