Each of the following defines a relation on N:

x + 4y = 10 x, y ∈ N.

Determine whether above relation is reflexive, symmetric and transitive.

Dear Student

x + 4y = 10; where x, y∈N
R = {(x, y): x + 4y = 10; x, y∈N}
R = {(2, 2), (6, 1)}
It’sclearly seen (1, 1)∉R
Hence, R is not symmetric.
(x, y)∈R⇒x + 4y = 10
And (y, z)∈R⇒y + 4z = 10
⇒x–16z = -30

⇒(x, z)∉R
Thus, R is not transitive.
Thanks