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V.K.Balakrishnan

Introductory Discrete Mathematics

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  • Kabangu Kabanguhas quoted3 years ago
    range of a function is a subset of its codomain
  • Kabangu Kabanguhas quoted3 years ago
    the image of x and x is a preimage of y
  • Kabangu Kabanguhas quoted3 years ago
    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.
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