Class 11 Math: Relations and Functions Quick Revision Chapter Summary

Need to review the entire chapter before a test? This quick revision guide summarizes all the core concepts, topics, and equations taught in Class 11 Relations and Functions to help you refresh your memory instantly.

Core Topics At a Glance

### 📌 Ordered pairs and Cartesian product An ordered pair (a, b) consists of two elements in a specific order. The Cartesian product A x B is the set of all ordered pairs (a, b) such that a belongs to A and b belongs to B.

### 📌 Domain, Co-domain, and Range of relation A relation R from set A to set B is a subset of A x B. The Domain is the set of all first elements in R. The Range is the set of all second elements in R. The Co-domain is the entire set B.

### 📌 Function as special relation A function f from set A to B is a relation where every element of A has exactly one image in B. No two distinct ordered pairs in f can share the same first element.

### 📌 Types of real functions (modulus, signum, greatest integer) Real functions map real inputs to real outputs. Special functions include: Modulus |x| (returns absolute value), Signum sgn(x) (returns -1, 0, or 1 based on sign), and Greatest Integer [x] (returns the largest integer less than or equal to x).

### 📌 Sum and quotient of functions Operations on real functions. For two functions f and g, their sum, difference, product, and quotient are defined on the intersection of their individual domains. For quotient, the divisor function cannot be zero.

Key Formulas Mind Map

• Cartesian Product Cardinality: `n(A \times B) = n(A) \times n(B)` - Number of ordered pairs in Cartesian product....

Revision Checklist

1. Review the subtopic guides and outline notes.
2. Practice writing the key formulas from memory.
3. Solve at least 3 worked examples and check your steps.
4. Take a timed practice quiz to verify your speed.