Let the universe be all positive real numbers and consider the quantified proposition ∃x∀y(xy=1). Which of the following is correct?
(a)None of the options are correct
(b)The proposition is false because if x=3, and y=1/4, then xy≠1.
(c)The proposition is false because for any x, if y=1/(x+1), then xy≠1
(d)The proposition is true because if x=3 and y=1/3, then xy=1
(e)The proposition is true because for any x we can set y=1/x which gives xy=1.