Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
+1 vote
637 views
in Sets, Relations and Functions by (50.2k points)
closed by

Let R be relation defined on the set of natural number N as follows:

R = {(x, y): x ∈ N, y ∈ N, 2x + y = 41}. Find the domain and range of the relation R. Also verify whether R is reflexive, symmetric and transitive.

1 Answer

+1 vote
by (48.7k points)
selected by
 
Best answer

Given function: R = {(x, y): x ∈ N, y ∈ N, 2x + y = 41}.

So, the domain = {1, 2, 3, ….., 20} [Since, y ∈ N ]

Finding the range, we have

R = {(1, 39), (2, 37), (3, 35), …., (19, 3), (20, 1)}

Thus, Range of the function = {1, 3, 5, ….., 39}

R is not reflexive as (2, 2) ∉ R as 2 x 2 + 2 ≠ 41

Also, R is not symmetric as (1, 39) ∈ R but (39, 1) ∉ R

Further R is not transitive as (11, 19) ∉ R, (19, 3) ∉ R; but (11, 3) ∉ R.

Thus, R is neither reflexive nor symmetric and nor transitive.

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.

Categories

...