Answer to Question #255915 in Discrete Mathematics for htd

Question

Determine whether each set below is a function from X = {1, 2, 3, 4} to Y = {a, b, c, d}. If it is a function, find its domain and range, draw its arrow diagram, and determine if it is oneto-one (Injective), onto (Surjective), or both (Bijective).

(a) {(1, c), (2, a), (3, b), (4, c), (2, d)}

(b) {(1, c), (2, d), (3, a), (4, b)}

(c) {(1, d), (2, d), (4, a)}

(d) {(1, b), (2, b), (3, b), (4, b)}

Answer 1

one-to-one function is a function f that maps distinct elements to distinct elements

onto function is a function f that maps an element x to every element y

bijective function f: X → Y is a one-to-one (injective) and onto (surjective)

function is a binary relation between two sets that associates each element of the first set to exactly one element of the second set

a)

onto function

b)

bijective function

domain: {1,2,3,4}

range: {a,b,c,d}

c)

not one-to-one function and not onto function

d)

not one-to-one function and not onto function