Set theory
Cardinality
Number of elements in a set.
$$
\cap(A \cup B) = \cap(A) + \cap(B) - \cap(A \cap B)
\newline
\cap(A \cap B) = 0
$$
Subsets
Proper subsets
Improper subsets
Disjoint sets
$$
\cap(A \cap B) = 0
$$
Universal sets
Denoted by the synbol \(\xi\)
Power set
Product set
Set where all elements are tuples of elements from the original sets.
Example
$$
S
$$
Venn diagrams
Complement of set-
All elements outside a set
Union of sets-
\(\cup\) All elements in either set
Intersection of sets-
\(\cap\) All elements in both sets
Relative complement
$$
A \ B = { x: x \epsilon A and x \not\epsilon B } or \ =
$$
Symmetric difference
\(A \oplus B\)
Belongs to A + belongs to B, but not both
Methods of proof of sets
Venn diagrams proofs
Set membership table
Use basic laws or proven theorems
Last update:
June 11, 2023
Created: June 11, 2023
Created: June 11, 2023