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

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

RD Sharma Solutions Class 12 Maths Chapter 3 Exercise 3.3

Before designing textbook RD Sharma Solutions in accordance with the CBSE board’s prescribed syllabus, Kopykitab’s team of experts do extensive research on each topic.

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