Class 12 Mathematics — Chapter 1: RELATIONS AND FUNCTIONS

What you'll learn

• ▸Empty and Universal Relations
• ▸Reflexive Relations
• ▸Symmetric Relations
• ▸Transitive Relations
• ▸Equivalence Relations
• ▸Equivalence Classes and Partitions

Chapter Summary

--- PAGE 1 --- Chapter 1 RELATIONS AND FUNCTIONS ❖ There is no permanent place in the world for ugly mathematics ... . It may be very hard to define mathematical beauty but that is just as true of beauty of any kind, we may not know quite what we mean by a beautiful poem, but that does not prevent us from recognising one when we read it. — G. H. HARDY ❖ 1.1 Introduction Recall that the notion of relations and functions, domain, co-domain and range have been introduced in Class XI along with different types of specific real valued functions and their graphs. The concept of the term 'relation' in mathematics has been drawn from the meaning of relation in English language, according to which two objects or quantities are related if there is a recognisable connection or link between the two objects or quantities. Let A be the set of students of Class XII of a school and B be the set of students of Class XI of the same school. Then some of the examples of relations from A…

Practice Questions from this Chapter

Tap "Get Solution" on any question to ask our AI tutor.

1. Explain functions using everyday examples. Get Solution →
2. Show types of relations with drawings. Get Solution →
3. Give a non-math example of symmetry. Get Solution →
4. According to the text, what is the mathematical definition of a relation R from a set A to a set B? Get Solution →
5. A relation R in a set A is called an empty relation if which condition is met? Get Solution →
6. What is a universal relation R in a set A? Get Solution →
7. According to Definition 3, a relation R in a set A is reflexive if... Get Solution →
8. A relation R in a set A is called symmetric if which of the following is true? Get Solution →

Did you know?

• 💡 The equals sign (=) was invented in 1557 to avoid writing "is equal to".
• 💡 Ancient Romans did not have a symbol for zero in their number system.
• 💡 Infinity can be "countable" or "uncountable," meaning some infinities are larger.
• 💡 There are more irrational numbers than rational numbers, even though both are infinite.
• 💡 A googol is a number with one followed by one hundred zeros.

Frequently Asked Questions

Related Chapters