rule that assigns to every element in X a unique element in Y
Kabangu Kabanguhas quoted3 years ago
The set X is the domain of the function and the set Y is its codomain. If
Kabangu Kabanguhas quoted3 years ago
THEOREM 0.1.2 (De Morgan’s Laws)
(a) (A ∩ B)c = Ac ∪ Bc.
(b) (A ∪ B)c = Ac ∩ Bc.
Kabangu Kabanguhas quoted3 years ago
region in the rectangle (which represents the universal set) that is outside the ellipses that represent the three sets is the absolute complement of the union of these three sets.
Kabangu Kabanguhas quoted3 years ago
THEOREM 0.1.1 (Distributive Laws)
(a) A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C).
(b) A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C).
Kabangu Kabanguhas quoted3 years ago
A class C(X) of subsets of a set X is called a partition of X if (1) C(X) is pairwise disjoint, and (2) the union of the sets in C(X) is the set X
Kabangu Kabanguhas quoted3 years ago
Two sets are disjoint if and only if their intersection is empty.
Kabangu Kabanguhas quoted3 years ago
both set intersection and set union possess the associative property: (1) A ∩ (B ∩ C) = (A ∩ B) ∩ C and (2) A ∪ (B ∪ C) = (A ∪ B) ∪ C.