Set Theory Flashcards
1
Q
x ∈ A
A
x is an element of A
2
Q
A = {x1, x2, …, xn}
A
A is a set containing x1, x2, …, xn
3
Q
A = {x: P(x)}
A
A is the set of elements x satisfying property P
4
Q
A ⊆ B
A
A is a subset of B
5
Q
A ⊂ B
A
A is a proper subset of B (A is a subset of B and A does not equal B)
6
Q
Ø
A
null set or empty set
7
Q
φ(A)
A
the powerset of A (the set of all subsets of A)
8
Q
If A = {1,2}, what is the powerset of A?
A
φ(A) = {Ø, {1}, {2}, {1, 2}}
9
Q
If |A| = n, then what is |φ(A)|?
A
|φ(A)| = 2^n
10
Q
How do you prove A ⊆ B?
A
show that for every x ∈ A, that x ∈ B
11
Q
How do you prove A = B?
A
show that A ⊆ B and B ⊆ A
12
Q
What is the size of a set called?
A
the cardinality of a set
13
Q
∪
A
union
14
Q
∩
A
intersection
15
Q
A^c
A
complement, everything not contained in A
