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SETS - Coggle Diagram
SETS
Intersections
Some basic properties of intersections:
A ∩ B = B ∩ A.
A ∩ (B ∩ C) = (A ∩ B) ∩ C.
A ∩ B ⊆ A.
A ∩ A = A.
A ∩ ∅ = ∅.
A ⊆ B if and only if A ∩ B = A
Unions
Two sets can be "added" together. The union of A and B, denoted by A ∪ B, is the set of all things which are
members of either A or B.
Describing Sets
There are two ways of describing, or specifying the members of, a set. One way is by intensional definition, using a rule or semantic description:
A is the set whose members are the first four positive integers.
B is the set of colors of the French flag.
Membership
Main article: Element (mathematics)
The key relation between sets is membership – when one set is an element of another. If a is a member of B, this is denoted a ∈ B, while if c is not
a member of B then c ∉ B. For example, with respect to the sets A = {1,2,3,4}, B = {blue, white, red}, and F = {n
2 − 4 : n is an integer; and 0 ≤ n ≤
19} defined above,
4 ∈ A and 285 ∈ F; but
9 ∉ F and green ∉ B.
