2.1 Sets Flashcards
When are two sets equal
Two sets are equal if and only if they have the same elements.
Order does not matter and it does not matter if an element is repeated
Definition of subsets (A and B)
The set A is a subset of B, and B is a superset of A if and only if every element of A is an element of B
How do we show that A is a subset of B
Show that if x belongs to A then x also belongs to B
How do we show that A is not a subset of B
find a single x ∈ A such that
x is not in B
When is A a proper subset of B
Power Sets
The power set of a set S is the set of all subsets of S.
How many subsets does the empty set ∅ have
It has one subset, itself
P(∅)= {∅}
How many subsets does the singleton set {∅} have
It has two subsets, ∅ and itself {∅}
P({∅}) = {∅, {∅}}
n-tuples
Ordered collection
When are the cartesian products AxB and BxA equal?
Only when A= ∅ or B=∅ or A=B
A is a subset of the set B
a is an element of the set A
A is a proper subset of the set B.
A is a subset of B but A doesn’t equal B
T/F?
False, the empty set has no elements
T/F?
False, the set on the right has only one element, the number 0, not the empty set
T/F?
False, the empty set has no proper subsets
T/F?
True, Every element on the left is, vacuously an element of the set on the right. And the set on the right has an element, 0, that is not in the set on the left
False, the set on the right has only one element, the number 0, not the set containing the number 0
T/F?
False, for one set to be a proper subset of another, the two sets cannot be equal
True, every set is a subset of itself
The number of sets in a power set
2^(number of elements(cardinality))
Cardinality
The number of distinct elements in S.
