Subsets. Subsets are sort of like nested Russian dolls: the subset “fits inside” the set.
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Transcript of Subsets. Subsets are sort of like nested Russian dolls: the subset “fits inside” the set.
Subsets
Subsets
Subsets are sort of like nested Russian dolls:the subset “fits inside” the set.
Subsets
Set A is a subset of set B if all of the members in set A are also in set B.
set A = { 1, 2, 3 } set B = { 1, 2, 3, 4, 5, 6 }
Set A is a subset of set B A B
NOT a Subset
Set A is NOT a subset of set B if any member in set A is not also in set B.
set A = { 1, 2, 9 } set B = { 1, 2, 3, 4, 5, 6 }
Set A is NOT a subset of set B because of the 9.
A B
Proper Subsets
If set A has fewer elements than set B, it is called a proper subset and we use
The idea is very similar to the concept of “less than”
‹
Improper Subsets
If they are the same set, it is called an improper subset and we use (or we could use =).
By definition, every set is a subset of itself.
A A
Generic Subsets
If we aren’t sure if it’s a proper subset or an improper subset, we use the generic subset symbol.
That way it is true either if it is proper or improper.
The Empty Set
Also by definition:
The empty set is a subset of every other set.
For every set A:
A
Listing Subsets
Let’s list all the subsets of the set {1, 2}
The proper subsets: {1}, {2}, and The improper subset: {1, 2}
A set with 2 elements has 22 or 4 subsets
A set with 2 elements has 22 – 1 or 3 proper
subsets
Listing Subsets
Let’s list all the subsets of the set {1, 2, 3}
The proper subsets: {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}The improper subset: {1, 2, 3}
A set with 3 elements has 23 or 8 subsets
A set with 3 elements has 23 – 1 or 7 subsets
Number of Subsets
If a set has n elements
The number of subsets will be 2n
The number of proper subsets will be 2n – 1
Vocabulary
Subset
Proper subset
Improper subset
Empty set