Question

Anyone please help me pleaseeee

Answer 1

R = { (x,y): 3x-y=0 }

The condition is 3x=y so that's not going to be any of these things.

R is reflexive if (x,x)∈R for all x.   Let's check.

3x - y = 3x - x = 2x ≠ 0  necessarily.   NOT REFLEXIVE

R is symmetric if (x,y)∈R → (y,x)∈R.   Let's check.

(x,y)∈R  so

3x-y = 0

y  = 3x

Is  (y,x)∈R.  That would be true if 3y-x=0

3y - x = 3(3x) - x = 8x ≠ 0 necessarily NOT SYMMETRIC

R is transitive if (x,y)∈R and (y,z)∈R → (x,z)∈R.   Let's check.

3x-y = 0  so y=3x

3y-z = 0 so z=3y = 9x

3x - z = 3x - 9x = -6x ≠ 0 necessarily   NOT TRANSITIVE