Question

Let x= (1,5,9) and Y=(3,4,7).

to. Define F:X → Y by specifying that
f(1)=4, f(5)=7, f(9)=4
Is f injective? Is f surjective? explain your answers

Answer 1

The function f is neither injective because it maps two elements of X to the same element of Y, nor surjective because not all elements of Y are covered.

Step-by-step explanation:

The function f maps set X to set Y, where X = (1,5,9) and Y = (3,4,7), and is defined as f(1) = 4, f(5) = 7, f(9) = 4. To determine if f is injective (or one-to-one), each element of X must map to a unique element of Y. Since f(1) and f(9) both map to 4, the function is not injective. To determine if f is surjective (or onto), every element of Y must be the image of some element of X under f. Since no element in X maps to 3 in Y, the function is not surjective.