## RD Sharma Class 12 Solutions Chapter 3 - Binary Operations (Ex 3.5) Exercise 3.5 - Free PDF

## FAQs on RD Sharma Class 12 Solutions Chapter 3 - Binary Operations (Ex 3.5) Exercise 3.5

**1. What are equivalence relations in Binary Operations?**

An equivalence relation on a set S is a relation on S which is reflexive, transitive, and symmetric, and the equivalence relation is denoted by.

**Example-** On the set X=a,b,c, the relation R=(a,a),(b,b),(c,c),(b,c),(c,b)is an equivalence relation.

The equivalence classes of the above relation are-

a=a,b=c=b,c

All equivalence classes for R are ab,c.

The relations that have “is equal to”, “is similar to”, “is congruent to”, “has the absolute value as”, “has the same cosine as” are all equivalence relations.

**2. What are the properties of binary relations?**

There are 4 properties of binary relations.

Let R be relation on a set, then:

If aRa, aA , R is reflexive.

If a,bA, if aRB then bRa, R is symmetric.

If a,b,cA, if aRb and bRc, then aRc, R is transitive.

If a,bA, if aRb and bRa, then a=b, R is anti-symmetric.

**3. Are Vedantu’s solutions helpful for practicing Maths questions in Class 12?**

Vedantu’s solutions are designed by subject experts and in accordance with the CBSE Board pattern in a step-by-step manner. The solutions are easy to understand as the students find the language familiar and easy to understand. Students can also refer to the revision notes provided by Vedantu to have a better understanding of the concept before solving the question since it is very important for the students to understand the concepts to the core in Class 12 as it lays a foundation for higher-level studies.

**4. Can a student rely completely on Vedantu’s study materials if he wants to score good grades in Maths in Class 12 Boards?**

Vedantu has lots of study materials available on its website which includes, syllabus for the subjects, revision notes for CBSE, ICSE, and other state boards, solved questions of various books, previous year question papers. So for the theoretical and conceptual part students should go through the chapter in textbooks first and then go for the revision notes. But the students can definitely rely on Vedantu for textbook solutions and previous year question papers.

**5. Is binary operations an important Chapter for class 12 boards?**

Binary Operations is the third chapter of RD Sharma Class 12 Maths and the first chapter of NCERT Maths with the name Functions and Relations. The whole chapter is very important for Class 12 and for National and State level competitive and entrance exams as well. In Boards, the weightage of the Chapter itself is a total of 8 marks. Therefore, students should not miss topics in this chapter. Students who want to focus on boards can refer to the NCERT Maths book and the student who wishes to study the concepts in-depth can refer to RD Sharma as detailed explanations of all concepts are there.