1. Q. Determine the truth values of each of these statements if the domain of each variable consists
of all real numbers. State the reason for your answers and give examples also in each part.
(a) There exist x such that For All y(xy =0)
(b) There exist x such that There exist y such that (x + y is not equal to y + x)
(c) For All x (x is not equal to 0 --> There exist y such that (xy = 1))
(d) There exist x such that For All y (y is not equal to 0 --> xy = 1)
(e) For All x, there exist y such that (x + y = 1)
Solution
(a) 1 (b) 0 (c) 1 (d) 1 (e) 1