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Class 12 Relations and Functions Concepts

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Class 12 Relations and Functions Concepts

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Questions and Answers

What is the mathematical definition of a relation R from a set A to a set B?

A relation is the intersection of sets A and B

A relation is the union of sets A and B

A relation is a subset of set A

A relation is a subset of the cartesian product A × B (correct)

If no element of set A is related to any other element of set A, what is the name given to this type of relation?

Invertible Relation

Functional Relation

Universal Relation

Trivial Relation (correct)

Which of the following statements is true about the empty relation in a set A?

The empty relation is a non-empty subset of A × A

The empty relation is denoted by R = A × A

No element in set A is related to any other element in set A (correct)

Every element in set A is related to every other element in set A

What does it mean if a relation R from a set A to a set B is called the universal relation?

Each element in set A is related to every element in set B Signup and view all the answers

If a relation R from a set A to a set B is not empty but not universal either, what type of relation does it represent?

Partial Relation Signup and view all the answers

What type of relation is a relation R in a set A if it is reflexive, symmetric, and transitive?

Equivalence relation Signup and view all the answers

Given a function f : X → Y, what makes f a one-to-one function?

The images of distinct elements in X are distinct Signup and view all the answers

What defines a function f : X → Y as onto?

Every element in Y is the image of some element in X Signup and view all the answers

In the context of functions, what does it mean for a function to be invertible?

The function is both one-to-one and onto Signup and view all the answers

What characterizes a binary operation ∗ on a set A?

It maps pairs of elements from A to A Signup and view all the answers