Functions: Injective, Surjective, and Bijective

The video tutorial explains how to map functions from a set with elements 1 and 2 to a set with elements a, b, and c using two-line notation. It covers the process of writing these functions, determining possible outputs, and categorizing them as injective, surjective, or bijective. The tutorial concludes that there are nine possible functions, six of which are injective, none are surjective, and none are bijective.

How many possible functions can be created when mapping from a set with elements 1 and 2 to a set with elements a, b, and c?

• 12

• 9

• 6

• 3

In two-line notation, what do the rows represent?

• Only inputs

• Outputs and inputs

• Only outputs

• Inputs and outputs

Which of the following is true about injective functions?

• They map every element of the codomain to the same element in the domain

• They do not have repeated elements from the codomain in the range

• They map every element of the domain to the same element in the codomain

• They have repeated elements in the codomain

How many of the nine functions are injective?

• 9

• 6

• 3

• 0

What is a characteristic of surjective functions?

• They map every element of the codomain to the same element in the domain

• They have repeated elements in the codomain

• They map every element of the domain to the same element in the codomain

• They do not miss elements from the codomain in the range

Why are none of the nine functions surjective?

• None of the elements are mapped

• There are more elements in the domain than in the codomain

• All elements are mapped to the same element

• There are more elements in the codomain than in the domain

How many functions are neither injective nor surjective?

• 0

• 9

• 6

• 3

Which functions are neither injective nor surjective?

• f sub 4 through f sub 9

• f sub 1 through f sub 3

• All functions

• None of the functions

What defines a bijective function?

• It is only injective

• It is neither injective nor surjective

• It is both injective and surjective

• It is only surjective

Are any of the nine functions bijective?

• Yes, all of them

• Yes, some of them

• Only one of them

• No, none of them