Up until I started writing this question, I have been attempting to teach myself these discrete math concepts, but now I want clarification on a question.
From the book:
Suppose that the domain of $Q$(x, y, z) consists of triples x, y, z, where x = 0, 1, or 2, y = 0 or 1, and z = 0 or 1. Write out these propositions using disjunctions and conjunctions.
c) $\exists z\neg Q(0, 0, z)$
d) $\exists x\neg Q(x, 0, 1)$
My answers to these:
c) $\neg [Q(0, 0, 0) \lor Q(0, 0, 1)]$
d) $\neg [Q(0, 0, 1) \lor Q(1, 0, 1) \lor Q(2, 0, 1)]$
I probably did not need to show both answers, as they perhaps make the same mistake.
What I did was rearrange the statement $\exists z\neg Q(0, 0, z)$ into $\neg\forall xQ(0,0,z)$ and since the "for all" statement I used the conjunction between each predicate, and then since everything in the parentheses is negated I switched them all to disjunctions (De Morgan's laws).
I switched to the answers in the back:
c) $\neg Q(0, 0, 0) \lor \neg Q(0, 0, 1)$
Is this not equivalent to:
$\neg [Q(0,0,0) \land Q(0,0,1)]$
Their answer to (d) is very much the same.
So is my answer wrong?
Also, I am not sure which tags to use for this question.. this subject is very new to me.