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.

Question

Philoid · Accepted Answer

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

Now, 2x + y = 41

⇒ y = 41 - 2x (i)

Since x ∈N, y ∈N from (i) we get the relation

R = {(1,39),(2,37),(3,35),(4,33),(5,31),(6,29),(7,27),(8,25),

(9,23),(10,21),(11,19),(12,17),(13,15),(14,13),(15,11),

(16,9),(17,7),(18,5),(19,3),(20,1)}

Domain(R) ={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}

Range(R) ={1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,

37,39}

R is not reflexive ∵ (1,1),(2,2)…(20,20) ∉ R

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

R is not transitive ∵ (12,17),(17,7) ∈ R but (12,7) ∉ R

Hence, R is neither reflexive nor symmetric nor transitive.

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