Class 11 Applied Mathematics Chapter 4 Handwritten Notes

The handwritten notes on Class 11 Applied Mathematics Chapter 4 Relations have been carefully prepared for quick revision, according to the latest 2026-27 CBSE syllabus. The PDF covers ordered pairs, Cartesian products, relations, domain, range, equivalence relation tests and functions.

• Best for one-shot revision: ordered-pair rules, relation properties and function tests stay in one PDF.
• Aligned to 2026-27: follows the current Class 11 Applied Mathematics Unit 2 scope.
• Exam ready: proof checks for reflexive, symmetric and transitive relations are placed close to examples.

Relations Handwritten Notes: What the PDF Covers

Relations starts with the idea that order matters. The chapter first explains ordered pairs, then uses them to build Cartesian products and relations between two sets.

Ordered Pair and Cartesian Product in Relations

An ordered pair is written as (a, b), where a is the first member and b is the second member. The order carries meaning, so (pencil, Rs. 1) is different from (Rs. 1, pencil).

The Cartesian product A x B lists every possible pair with first entry from A and second entry from B. A x B is usually not the same as B x A. Count the pairs by multiplying the number of elements in the two sets.

• If A = {a, b, c} and B = {1, 2}, then A x B has 6 pairs.
• If one set is empty, the Cartesian product is empty.
• For three sets, use ordered triplets such as (a, b, c).

Relations and Functions Quick Revision for Class 11

Source: Magnet Brains on YouTube

Domain, Range and Co-Domain in Relations

A relation R from set A to set B is a subset of A x B. If (a, b) belongs to R, then b is the image of a under R. Students can write this as a R b.

Domain means all first entries used in the relation. Range means all second entries used in the relation. Co-domain means the full target set B, so the range is always a subset of the co-domain.

Reflexive, Symmetric and Transitive Relation Tests

Relation-property questions need a definition-by-definition check. A relation is reflexive when every self-pair (a, a) is present. It is symmetric when every pair has its reverse pair.

A relation is transitive when (a, b) and (b, c) force (a, c). An equivalence relation must pass all three tests. If even one test fails, it is not an equivalence relation.

• Triangle similarity is reflexive, symmetric and transitive.
• The subset relation is reflexive and transitive, but not symmetric.
• The relation 3 divides a - b on integers is an equivalence relation.

Functions as Special Relations in Class 11 Applied Mathematics

A function from A to B is a special relation where every element of A has exactly one image in B. This is the easiest test: scan the first entries and check whether any input gets two outputs.

For example, {(1, 2), (2, 3), (3, 4), (4, 5)} is a function. The relation {(1, 1), (1, 2), (1, 3)} is not a function because the input 1 has three images.

• Every function is a relation.
• Every relation is not a function.
• Domain must be fully used in a function from A to B.

How to Revise Relations Before Class Tests

Use the Relations handwritten notes in two passes. First, revise definitions and examples. Second, practise one question each on ordered-pair equality, Cartesian-product listing, domain-range finding and relation-property testing.

• Write the equality rule for ordered pairs once.
• List A x B and B x A for a small example.
• Circle first entries for domain and second entries for range.
• Test reflexive, symmetric and transitive properties separately.
• Finish with one function-or-not-a-function question.

Related Resources for Relations Class 11

Applied Mathematics Handwritten Notes for All Chapters