For each of the following binary relations rho on Z decide w

For each of the following binary relations rho on Z, decide which of the given ordered pairs belong to rho. x rho y doubleheadarrow x|y, (2, -6), (3, 5), (8, 4), (4, 8) x rho y doubleheadarrow x and y art are relatively prime; (5, 8), (9, 16), (6, 8), (8, 21) x rho y doubleheadarrow gcd (x, .y) = 7; (28, 14), (7, 7), (10, 5), (21, 14) x rho y doubleheadarrow x^2 + y^2 = z^2 for some integer; (1, 0), (3, 9), (2, 2), (-3, 4) x rho y doubleheadarrow x is a number from the Fibonacci sequence; (4, 3), (7, 6), (7, 12), (20, 20)

Solution

2.
(a)
Its not clear what the relation is, so I am taking it as x/y, or, x is divisible by y
(8, 4) belongs to p, since 8 is divisible by 4.

(b)
(5, 8), (9, 16), (8, 21) all belong to p, since all these 3 pairs are co prime.

(c)
(7, 7), (21, 14) belong to p, since the gcd of each pair is 7.

(d)
(1, 0), (-3, 4) belong to p, since
1^2 + 0^2 = 1^2, and
(-3)^2 + 4^2 = 5^2

(e)
None, as none of the xs exist in the fibonacci sequence.