Can some tell whey these relations are not functions.?

Question

R= {(x,y) is in N X N: x is less or equal to y} (N=natural number)

R={(x,y) is in Z X Z: y^2=x} (Z= integer)

Answer 1

1) R = {(x,y) is in N X N: x is less or equal to y} (N = natural number)

(1, 5) and (1, 4) are both in R. One x value has at least 2 y values, so this is not a function.

2) R={(x,y) is in Z X Z: y^2=x} (Z= integer)

(1, 1) (1, -1) are both in R. One x value has two y values, so this is not a function.

Answer 2

They aren't because two different y values can work with the same x.

For example 4 <= 10 but 4 <= 11 also

And 16 = 4^2 but 16 also = (-4)^2

Answer 3

Well, for your first set, (1,3) and (1,2) are both members. This is a violation of functions since functions must be single valued(one point gets sent to only one point). For your second example, (4,2) and (4,-2) are both points and violate the one value rule the same as your first example.