so I'm working through homework questions for proofs class and unsure if I'm correct in my interpretation. I would really appreciate feedback. The questions states: Write the full meaning in English and decide whether True or False
a) ∀x∀y(x ≥ y)
False: for all x and for all y, there is an x which is greater/equal then y.
b) ∃x∃y(x ≥ y)
True: There exists an x and a y, in which an x is greater/equal then y.
c) ∃y∀x(x ≥ y)
True: There exists a y for all of x, where x greater/equal then y
d) ∀x∃y(x ≥ y)
True: For all x, there is a y, in which x greater/equal then y
e) ∀x∃y(x^2 + y^2 = 1)
False: For all x, there is a y in which x^2+y^2 = 1
f) ∃x∀y(x^2 + y^2 = 1)
False: There exists an x for all y in which x^2+y^2 = 1