Functions: Domain, Injective, Surjective

The video tutorial explains how to map functions from a set with elements {1, 2, 3} to a set with elements {a, b} using two-line notation. It details the eight possible functions, discusses injective and surjective properties, and analyzes which functions meet these criteria. The tutorial concludes that none of the functions are injective, six are surjective, and none are bijective due to the mismatch in the number of elements between the domain and codomain.

What is the domain of the functions discussed in the video?

• Set with elements x, y, and z

• Set with elements 4, 5, and 6

• Set with elements 1, 2, and 3

• Set with elements a and b

How many possible functions can be created from the given domain and codomain?

• 8

• 6

• 10

• 4

Which of the following is true about injective functions?

• They map every element of the domain to exactly one element of the codomain.

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

• They map every element of the codomain to at least one element from the domain.

• They have repeated elements from the codomain in the range.

Why are none of the functions injective?

• Because they miss elements from the codomain in the range.

• Because they map every element of the domain to the same element of the codomain.

• Because they map every element of the codomain to multiple elements from the domain.

• Because they have repeated elements from the codomain in the range.

What is a characteristic of surjective functions?

• They map every element of the codomain to exactly one element from the domain.

• They have repeated elements from the codomain in the range.

• They miss elements from the codomain in the range.

• They map every element of the domain to a unique element of the codomain.

Which functions are not surjective?

• Functions 1 and 2

• Functions 7 and 8

• Functions 3 and 4

• Functions 5 and 6

How many functions are neither injective nor surjective?

• 2

• 8

• 4

• 6

What is a bijective function?

• A function that is only injective

• A function that is both injective and surjective

• A function that is neither injective nor surjective

• A function that is only surjective

Why can't there be a bijective function in this scenario?

• Because all functions are injective.

• Because there are more elements in the codomain than in the domain.

• Because there are fewer elements in the codomain than in the domain.

• Because all functions are surjective.

How many functions are bijective?

• 6

• 0

• 2

• 4