RD Sharma Solutions For Class 12 Maths Exercise 3.3 Chapter 3 Binary Operations (Updated for 2021-22)

RD Sharma Solutions Class 12 Maths Chapter 3 Exercise 3.3: The identity elements for binary operations are explained in the third exercise in Chapter 3. The RD Sharma Solutions for Class 12 Chapter 3 Exercise 3.3 are provided in easy-to-understand language, which increases students’ grasping ability. Students can refer to RD Sharma Solutions Class 12 Maths Chapter 3 Binary Operations Exercise 3.3 PDF, which is available here, for more understanding on the concepts covered in this exercise.

Download RD Sharma Solutions Class 12 Maths Chapter 3 Exercise 3.3 PDF

RD Sharma Solutions Class 12 Maths Chapter 3 Exercise 3.3

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Access RD Sharma Solutions For Class 12 Maths Chapter 3 – Binary Operations Exercise 3.3 Questions With Solution

1. Find the identity element in the set I+ of all positive integers defined by a * b = a + b for all a, b ∈ I+.

Solution:

Let e be the identity element in I+ with respect to * such that

a * e = a = e * a, ∀ a ∈ I+

a * e = a and e * a = a, ∀ a ∈ I+

a + e = a and e + a = a, ∀ a ∈ I+

e = 0, ∀ a ∈ I+

Thus, 0 is the identity element in I+ with respect to *.

2. Find the identity element in the set of all rational numbers except – 1 with respect to * defined by a * b = a + b + ab

Solution:

Let e be the identity element in I+ with respect to * such that

a * e = a = e * a, ∀ a ∈ Q – {-1}

a * e = a and e * a = a, ∀ a ∈ Q – {-1}

a + e + ae = a and e + a + ea = a, ∀ a ∈ Q – {-1}

e + ae = 0 and e + ea = 0, ∀ a ∈ Q – {-1}

e (1 + a) = 0 and e (1 + a) = 0, ∀ a ∈ Q – {-1}

e = 0, ∀ a ∈ Q – {-1} [because a not equal to -1]

Thus, 0 is the identity element in Q – {-1} with respect to *.

Binary Operations Ex 3.3 Q3

Binary Operations Ex 3.3 Q4

We have provided complete details of RD Sharma Solutions Class 12 Maths Chapter 3 Exercise 3.3. If you have any queries related to CBSE Class 12 Exam, feel free to ask us in the comment section below.

FAQs on RD Sharma Solutions for Class 12 Maths Chapter 3 Exercise 3.3

How many questions are there in RD Sharma Solutions for Class 12 Maths Chapter 3 Exercise 3.3?

There are a total of 4 questions in RD Sharma Solutions for Class 12 Maths Chapter 3 Exercise 3.3.

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Yes, You can get RD Sharma Solutions for Class 12 Maths Chapter 3 Exercise 3.3 for free.

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