Question

Relation R in set A={1,2,3,......,13,14} defined as R={(x,y):3x-y=0}

Answer 1

The answer is,
A = {1, 2, 3 … 13, 14}
R = {(x, y): 3x − y = 0}
∴ R = {(1, 3), (2, 6), (3, 9), (4, 12)}
R is not reflexive since (1, 1), (2, 2) … (14, 14) ∉ R.
Also, R is not symmetric as (1, 3) ∈R, but (3, 1) ∉ R. [3(3) − 1 ≠ 0]
Also, R is not transitive as (1, 3), (3, 9) ∈R, but (1, 9) ∉ R.
[3(1) − 9 ≠ 0]
Hence, R is neither reflexive, nor symmetric, nor transitive.

Answer 2

Questions .Relation R in set A={1,2,3,......,13,14} defined as R={(x,y):3x-y=0}
answer. I think u have to want to know R Is a
reflexive, symmetric, transitive.

so . R= {(x+,y):3x-y=0}
Now change it in Rostar form
we get ➢
R={(1,3) (2,6) (3,9) (4,12)}
R is not [reflexive ]
because . (1,1) (2,2)(14,14) € to R
Also R is not [symmetric]
because (1,3)£R but (3,1)€ R
[3(3-1) not equal to zero

Also R Is Not [Transitive ]

(1,3 ) (3,9)£R
but (1,9) € R

[3(1)-9 not equal to zero ]
so R is not reflexive, not symmetric, not transitive.