Search results
16 wrz 2024 · What is a function in discrete mathematics? A function in discrete mathematics is a relation between a set of inputs (domain) and a set of possible outputs (range), such that each input is related to exactly one output.
A function is a rule that assigns each input exactly one output. We call the output the image of the input. The set of all inputs for a function is called the domain. The set of all allowable outputs is called the codomain. We would write f: X → Y to describe a function with name , f, domain X and codomain . Y.
Questions: 1.Consider the sets Aand Bwhere: A= fa2Zja= 2k, for some integer kg, B= fb2Zjb= 2j 2, for some integer jg. Does A= B? If yes, prove it. If no, explain why not. 2.Consider the sets A= f1;2;3g, B= fx;yg, and C= fu;vg. Let P(A) denote the powerset of A. Find each of the following: (a) P(A[B) (b) P(B C) (c) P(P(C)) (d) A (B\C) (e)(A B) C
EXAMPLE 1 The set V of all vowels in the English alphabet can be written as V = {a, e, i, o, u}. EXAMPLE 2 The set O of odd positive integers less than 10 can be expressed by. O = {1, 3, 5, 7, 9}. Sometimes the roster method is used to describe a set without listing all its members.
This le contains an English version of exercises in the course of Discrete mathematics. Most of the problems were prepared by Michael Kubesa, Tereza Kova rov a, and Petr Kov a r.
A discrete function is a type of function that is defined only at specific, separate points in its domain, typically involving integers or countable sets. This characteristic distinguishes it from continuous functions, which are defined over an interval and can take on any value within that range.
Functions A function f : A →B (pronounced “f taking A to B” or “f from A to B”) is a subset of A×B satisfying the following. f : A →B is a function precisely when each element x ∈A is matched to one value f(x) ∈B.
