Relations and Functions Class 11 Notes - Chapter 2 - GMS - Learning Simply
Students' favourite free learning app with LIVE online classes, instant doubt resolution, unlimited practice for classes 6-12, personalized study app for Maths, Science, Social Studies, video e-learning, online tutorial, and more. Join Telegram

# Relations and Functions Class 11 Notes - Chapter 2

Relations and Functions Class 11 Notes - Chapter 2 class 10 maths ncert solutions ncert solution of class 11 math class 10th math solution class 10 m
Please wait 0 seconds...
Scroll Down and click on Go to Link for destination
Congrats! Link is Generated

# Relations and Functions Class 11 Notes - Chapter 2

If P and Q are non-empty sets then the set of all ordered pairs (a, b) is called the Cartesian product of A and B [were a ∈ P and b ∈ Q]. It can be represented symbolically as P × Q = {(a, b) | a ∈ P and b ∈ Q}.

To get more details on Relations and Functions, .

Example

If P = {3, 4, 5} and Q = {6, 7}, then

• P × Q = {(3, 6), (4, 6), (5, 6), (3, 7), (4, 7), (5, 7)}
• Q × P = {(6, 3), (6, 4), (6, 5), (7, 3), (7, 4), (7, 5)}

Case 1:  Two ordered pairs are said to be equal if their corresponding first and second elements are equal, i.e. (p, q) = (m, n) if p = m and q = n.

Case 2: If n(P) = a and n (Q) = b, then n(P × Q) = a × b.

Case 3: If P × P × P = {(p, q, r) : p, q, r ∈ P}. Then, (p, q, r) is known as an ordered triplet.

### When Sets are said to be in a Relation?

If P and Q are two non-empty sets, then a Relation (R) from set P to set Q is a subset of set P × Q. In this relation, the set of all first elements in R is known as the domain of the relation (R) and the set of all second elements is known as the range of R.

• A relation (R) can be represented in either Roster or set builder form. The visual representation of a relation is done using an arrow diagram.
• If n(P) = a, n(Q) = b; then n(P × Q) = ab. Also, the total possible relations from set P to Q = 2ab.

For example: The set R = {(11, 12), (-12, 13), (11/2, 13)} is a relation. The domain = {11, -12,11/2} and its range = {12, 13}

### What are the Functions?

A relation from set P to Q is said to be a function of all the elements of set P have just one image in set Q. The expression f : P → Q denotes: f is a function from P to Q and the Domain and codomain of function (f) are represented by P and Q respectively.

Relations and Functions Class 11 Practice Questions

1. Let P = {-11, 12, 13} and Q = {11, 23}. Determine
• P × Q
• Q × P
• Q × Q
• P × P
1. If A = {y : y < 4, y ∈ N}, B = {y : y ≤ 2, y ∈ W(set of whole numbers)}. Find (A ∪ B) × (A ∩ B).
2. If P = {y : y ∈ W, y < 4}, Q = {y : y ∈ N, 2 < y < 6}, and R = {3, 6}. Find (i) P × (Q ∩ R) (ii) P × (Q ∪ R).
3. Find the values of p and q, if (2p + q, p – q) = (8, 3).
4. Given P = {11, 12, 13, 14, 15}, S = {(a, b) : a ∈ P, b ∈ P}. Find the ordered pairs satisfying:
• a + b = 5
• a + b < 5
• a + b > 8
1. If R1 = {(a, b) | b = 2a + 7, a ∈ R and – 5 ≤ a ≤ 5} is a relation. Find the domain and Range of R1.
2. If R3 = {(a, a ) | a is a real number} is a relation. Find the domain and range of R3.

Below Are Video Lessons Of Chapter 2 👇👇👇👇

Get All Video Lectures At Our YT Channel :- Goyanka Maths Study

## About the Author

At the helm of GMS Learning is Principal Balkishan Agrawal, a dedicated and experienced educationist. Under his able guidance, our school has flourished academically and has achieved remarkable milestones in various fields. Principal Agrawal’s visio…

### Post a Comment

Cookie Consent
We serve cookies on this site to analyze traffic, remember your preferences, and optimize your experience.
Oops!
It seems there is something wrong with your internet connection. Please connect to the internet and start browsing again.
AdBlock Detected!
We have detected that you are using adblocking plugin in your browser.
The revenue we earn by the advertisements is used to manage this website, we request you to whitelist our website in your adblocking plugin.
Site is Blocked
Sorry! This site is not available in your country.