I've been working on real analysis for a short time and am really struggling to find the supremum and infimum of these sets (or if they exist at all)

the set of rational numbers in the interval [0,1]

the set of real numbers in the half open interval ]0,1]

the half line x ∈ R | x≤0

S={(x^2+y^2/xy)|x>0, y>0}

thank you!