Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • 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.

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

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

Answers (1)

Here, R = \{ (x, y): x \in N, y \in N, 2x + y = 41 \}  

So, the domain D= \{ 1, 2, 3, \ldots .., 20 \} \\

And the Range = \{ 1, 3, 5, \ldots .., 39 \} \\

Here, (2, 2) \notin \: \: R\: \: as\: \: 2 \times 2 + 2 \neq 41. Therefore, R is not reflexive. 

Again, (1, 39) \in R \: \: but\: \: (39, 1) \: \: \notin R. So, R is not symmetric.

Again, (11, 19) \notin R, (19, 3) \notin R; but (11, 3) \notin R. So, Further R is not transitive.

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

Posted by

infoexpert22

View full answer

Similar Questions

Latest Question