# 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 âˆˆ P and b âˆˆ Q]. It can be represented symbolically as P Ã— Q = {(a, b) | a âˆˆ P and b âˆˆ Q}.

To get more details on Relations and Functions, visit here.

Example

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

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

Case 1: Â 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 Ã— Q) = a Ã— b.

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

Also Refer:Â NCERT Solutions for Class 11 Maths Chapter 2

### 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 Ã— 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 Ã— 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}

To know more about Relations and its types, visit here.

### 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 â†’ 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 Ã— Q
• Q Ã— P
• Q Ã— Q
• P Ã— P
1. If A = {y : y < 4, y âˆˆ N}, B = {y : y â‰¤ 2, y âˆˆ W(set of whole numbers)}. Find (A âˆª B) Ã— (A âˆ© B).
2. If P = {y : y âˆˆ W, y < 4}, Q = {y : y âˆˆ N, 2 < y < 6}, and R = {3, 6}. Find (i) P Ã— (Q âˆ© R) (ii) P Ã— (Q âˆª 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 âˆˆ P, b âˆˆ P}. Find the ordered pairs satisfying:
• a + b = 5
• a + b < 5
• a + b > 8
1. If R1 = {(a, b) | b = 2a + 7, a âˆˆ R and â€“ 5 â‰¤ a â‰¤ 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.

## Frequently asked Questions on CBSE Class 11 Maths Notes Chapter 2: Relations and Functions

### What is a â€˜Relationâ€™ in mathematical terms?

In Mathematics, the relation is the relationship between two or more set of values.

### What is a â€˜Functionâ€™ in mathematical terms?

In Mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

### What are the uses of â€˜Functionsâ€™?

Some of the important types of functions are: 1. Many to one function.2. One to one function.3. Onto function.4. One and onto function.5. Constant function.6. Identity function.