Question

Student Activity check Whether the following functions to one are One and onto 1) X = {1, 2, 3, 4} y = {a,b} and f={(1,a),(2,a),(3,a),(4,a)​

Answer 1

Answer:

Definition: One-to-One (Injection)

A function f:A→B is said to be one-to-one if

f(x1)=f(x2)⇒x1=x2(5.3.1)

for all elements x1,x2∈A. A one-to-one function is also called an injection, and we call a function injective if it is one-to-one. A function that is not one-to-one is referred to as many-to-one.

Answer 2

its one to one but not onto

because every element in x has its image in b

but every element in b does not have image in a