I was given this on a practice exam:
Decide whether each of the following expressions is valid or invalid. Justify your answers (i.e.,if invalid, give an interpretation for which the expression is false;if valid explain why the expression is true for all interpretations.
(a) $[(\forall x)P(x) \vee (\exists x)Q(x)] \implies (\forall x)[P(x) \vee Q(x) ]$
(b) $[(\exists x)Q(x) \implies (\forall x)P(x)] \implies (\exists x)[P(x) \vee Q(x)]$
The answers are:
a. False: Let P(x)= "x != x" and Q(x) = "x=1"
b. False: Let "There exists x Q(x)" be false and "There exists x P(x)" be false.
I don't understand what he's doing. What am I not seeing?