Disclaimer: This is a college course of mine in which the homework is scrutinized by the professor and worth 30% of our grade. I've done all the homework problems by myself except these 2. Do not, in any way, tell me how to do it. It's okay to explain something that my attempt shows I'm fuzzy on, or to remind me of a certain fact of math reasoning that could lead me in the right direction. Just be wary. Here is a link to the assignment, just in case my writing transcript doesn't do it justice: http://www.math.washington.edu/~folland/hw4.pdf(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

(I don't know how to make all the fancy symbols)

(A disunion B = A disunion C) and (A union B = A union C) equivalent to B = C

2. Relevant equations

?

3. The attempt at a solution

I'm thinking proof by contradiction

(A disunion B ≠ A disunion C) or (A union B ≠ A union C) equivalent to B ≠ C

It seems like common sense but I can't figure out how to explain it. "Pictures are not proofs," my professor says. I mean, obviously if the intersection of A and B is equal to the intersection of B and C then B=C, right?

Help me get on the right track here.

1. The problem statement, all variables and given/known data

Suppose that A is a subset of Z (integers). Write the following statements entirely in symbols using the quantifiers A (an upside down A) and E (a backwards E). Write out the negative of this statement in symbols.

There is a greatest number in the set A.

Give an example of a set A for which this statement is true. Give another example for which it is false.

2. Relevant equations

The upside down A means "for each" and the backwards E means "there exists a". Just in case you didn't know.

3. The attempt at a solution

So.........

The part that has me stuck is the "There is a greatest number...". I can't figure out how that would be written in symbols. It would come in the predicate, no doubt. Something like {............. : a_{k}> a_{k+1}}. Nothing in the book speaks of writing a proof for "there is a greatest number". I'm even sure I understand what that means. Does it mean we have a set that goes something like 1,2,3,..........,n and n is the greatest number? If so, what sort of predicate says that?

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# Homework Help: A few homework problems (due Friday!)

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