pre calculus question !!

Question

Let S be a nonempty subset of plane R^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)

Answer 1

The contrapositive of "if P then Q" is "if not Q then not P".

 

The contrapositive is equivalent to the given statement.

 

So, the points in S must satisfy statement (II). 

 

ANSWER:  (a)