C959 Discrete Math 1 questions with 100% correct answers

Set Difference A - B, the set containing those elements that are in A but not in B Set Symmetric Difference A ⊕ B: the set of elements that are a member of exactly one of A and B, but not both. An alternative definition of the symmetric difference operation is: A ⊕ B = ( A - B ) ∪ ( B - A ) Set Complement the set of all elements in U that are not elements of A. An alternative definition of A is U - A. Set Intersection A ∩ B: the resulting set that contains all elements are in both A and B Set Union A ∪ B: the union of all elements in A and in B Domain (function) The set of all possible input values for the function Target (function) the set a function maps into Range (function) he subset of the target set (codomain) and consists of all of the mapped points Function equality if two functions have the same domain, the same codomain, and map each element of their common domain to the same element in their common codomain Floor function (L backwards L): round down, the largest integer y such that y ≤ x. Ceiling function (upside down L, backwards upside down L): round up, the smallest integer y such that x ≤ y. Surjective Function target is equal to the range; A function f: X - Y is surjective if for every element y of Y there exists an element x of X such that y = f(x). Injective Function a category of functions that map all inputs in the domain to distinct outputs but not necessarily all elements in the range. Note: This function type is also known as a "one-to-one function". Bijective Function is both injective and surjective Inverse functions only possible if function is bijective; found by swapping the values of X with the values of Y To algebraically solve for an inverse, use the following algorithm: - Replace f(x) with y - Interchange x and y - Solve for y. - Replace y with f−1(x) composition The process of applying a function to the result of another function