Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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.

share|improve this question
add comment

1 Answer 1

up vote 1 down vote accepted

The answers you suggest are not, each time for basically the same reason.

Take the first. Your translation says that $Q(0,0,z)$ fails at both $z=0$ and $z=1$. But the existential statement you are translating says that $Q(0,0,z)$ fails somewhere.

You ask whether $\lnot Q(0, 0, 0) \lor \lnot Q(0, 0, 1)$ is equivalent to $\lnot [Q(0,0,0) \land Q(0,0,1)]$. Indeed they are equivalent. However, you wrote earlier that your answer to (c) was $\lnot [Q(0,0,0) \lor Q(0,0,1)]$.

share|improve this answer
    
Okay, I think my miscalulation occurred when I said "not for all" and then I magically threw in another negation and said "not not for all," thanks for the feedback. –  Leonardo Dec 13 '12 at 4:52
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.