0 votes
6 views
in Relations and Functions by (22.3k points)
closed by

(i) Give a relation on a set A = {1,2,3,4} which is reexive , symmetric and not transitive. 

(ii) Show that ƒ : [-1,1] → R given by

f(x) = \(\frac{x}{x+2}\) is  one-one.

(iii) Let ‘*’ be a binary operation on Q dened by a*b = a*b = \(\frac{ab}{6}\) ’.Find the inverse of 9 with respect to ’ * ’.

1 Answer

+1 vote
by (23.3k points)
selected by
 
Best answer

R = {(1,1)(2,2),(3,3),(4,4),(1,2),(2,1),(1,3),(3,1)}

f(x1) = f(x2) ⇒ \(\frac{x_1}{x_1+2}\) =\(\frac{x_2}{x_2 + 2}\)

⇒ x1(x2+ 2) = x2 (x1 + 2)

⇒ x1x2 + 2x1 = x2x1 + 2x2

⇒2x1 = 2x2 ⇒ x1 = x2

Hence one-one

(iii) a*e = a⇒ \(\frac{ae}{6}\) = a ⇒ e=6

e*a = a⇒ \(\frac{ea}{6}\) = a ⇒ e = 6

identity element = 6

a*b = e ⇒ 9*b = 6 ⇒ \(\frac{9b}{6}\) = 6 ⇒ b = \(\frac{36}{9}\) = 4

b*a = e ⇒ b*9  = 6 ⇒ \(\frac{b9}{6}\) = 6 ⇒ b = \(\frac{36}{9}\) = 4

Inverse element = b = 4

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...