Answer to Question #72480 in Abstract Algebra for dslhl

Question

Let S be a nonempty subset of plane 2 \ , it is known that every point ( , ) x y in S
satisfies “if x > 0 , then y > 0 ”. Consider the following properties possibly satisfied
by points( , ) x y in S :
(I) If x ≤ 0 , then y ≤ 0 .
(II) If y ≤ 0 , then x ≤ 0 .
(III) If y > 0 , then x > 0 .
Which of the above properties will have to be satisfied by all points( , ) x y in S?
(a) (II) only
(b) (III) only
(c) (I) and (II)
(d) (I) and (III)
(e) (II) and (III)