Mappings and Functions Analysis

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

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

• 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.

What is the key difference between a function and a general relation?

• A function allows multiple images for each domain element.

• A function requires each domain element to have a unique image.

• A relation requires each range element to have a unique pre-image.

• A relation allows only one-to-one mappings.

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

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

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

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

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

In a one-to-one mapping, what happens if an element in the domain has no image?

• The mapping is not considered a function.

• The mapping becomes one-to-many.

• The mapping is still considered one-to-one.

• The mapping becomes many-to-one.

What is the result of a one-to-one mapping?

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

• 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.

• Each element in the range has multiple pre-images.

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 domain maps to multiple elements in the range.

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

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

What is a characteristic of a one-to-many mapping?

• Each element in the range has a unique pre-image.

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

• 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.

In a one-to-many mapping, what is true about the domain?

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

• 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.

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

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

• Each element in the range is an image of a unique element in the domain.

• Multiple elements in the domain map to a single element in the range.

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

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

In a many-to-one mapping, what is true about the range?

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

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

• Each element in the range is an image of a unique element in the domain.

• Each element in the range has multiple pre-images.