Function and Mapping Types

The video tutorial explains the concept of functions and relations, focusing on different types of mappings: one-to-one, one-to-many, many-to-one, and many-to-many. It clarifies which mappings qualify as functions and which do not, emphasizing that one-to-one and many-to-one mappings are functions, while one-to-many and many-to-many mappings are not.

What is the primary condition for a relation to be considered a function?

• Every element in the domain has one and only one image in the range.

• Every element in the domain has multiple images in the range.

• Every element in the range has multiple pre-images in the domain.

• Every element in the range has one and only one pre-image in the domain.

In a one-to-one mapping, what is true about the elements in the domain and range?

• Each element in the range is an image of multiple elements in the domain.

• Each element in the range has no pre-image in the domain.

• Each element in the domain maps to multiple elements in the range.

• Each element in the domain maps to a unique element in the range.

Which type of mapping ensures that a relation is always a function?

• Many-to-many

• One-to-one

• One-to-many

• None of the above

Why is a one-to-many mapping not considered a function?

• Because each element in the range has no pre-image.

• Because each element in the range has multiple pre-images.

• Because each element in the domain maps to a unique element in the range.

• Because each element in the domain maps to multiple elements in the range.

In which mapping type does an element in the domain have more than one image in the range?

• None of the above

• One-to-many

• One-to-one

• Many-to-one

In a many-to-one mapping, what can be said about the relation?

• It is a function because each element in the range has no pre-image.

• It is not a function because each element in the range has multiple pre-images.

• It is a function because each element in the domain has one and only one image in the range.

• It is not a function because each element in the domain maps to multiple elements in the range.

What is the result of a many-to-one mapping in terms of function classification?

• It depends on the elements.

• It is a function.

• It cannot be determined.

• It is not a function.

What is the key difference between one-to-one and many-to-one mappings?

• Many-to-one has a unique image for each domain element.

• One-to-one has a unique image for each domain element.

• Many-to-one has multiple images for each domain element.

• One-to-one has multiple images for each domain element.

What characterizes a many-to-many mapping?

• Multiple elements in the domain map to multiple elements in the range.

• Each element in the domain maps to a unique element in the range.

• Each element in the range is an image of multiple elements in the domain.

• Each element in the domain maps to multiple elements in the range.

Which mapping type results in a relation not being a function due to multiple images?

• Many-to-many

• One-to-one

• One-to-many

• Many-to-one