1. ## Proof Checking Help

Its me again, sorry. I was wondering would proof checking work be allowed in these forums rules as I have done the working out but was wondering would someone be able to go through it and just tell me which ones are wrong without telling me what the answer is so that I can go back too that question and attempt it again, as doing it myself teaches myself and someone giving me an answer is just pointless as it wont benefit me in anyway, agree? Anyway here is the key;

Key
$\displaystyle Stores = $$\displaystyle \{Tesco, Lidl, Asda, Coop, Aldi \} \displaystyle Department =$$\displaystyle \{Sales, HR, Management \}$
$\displaystyle Place = $$\displaystyle \{Cardiff, Bristol \} \displaystyle Teams =$$\displaystyle \{1, 2, 3 \}$

$\displaystyle 1 =$
$\displaystyle \{Tesco, Lidl \}$
$\displaystyle 2 = $$\displaystyle \{Aldi, Asda, Lidl \} \displaystyle 3 =$$\displaystyle \{Coop, Lidl, Aldi \}$

$\displaystyle A\cup B\ = \{Tesco, Lidl, Aldi, Asda \}$
$\displaystyle A\cup B\cup C\ = \{Tesco, Lidl, Aldi, Asda, Coop \}$
$\displaystyle B\cap C\ = \{Aldi, Lidl \}$

$\displaystyle Stores \setminus B = \{Tesco, Coop \}$

$\displaystyle The power set (Department) = \{\} \{Sales\} \{HR\} \{Sales, HR\} \{Management\} $$\displaystyle \{Sales, Management\} \{HR, Management\} \{Sales, HR, Management\} \displaystyle The Cartesian Product - Department x Place =$$\displaystyle \{Sales, Cardiff\} \{Sales, Bristol\} \{HR, Cardiff\}$$\displaystyle \{HR, Bristiol\} \{Management, Cardiff\} \{Management, Bristol\} \displaystyle (Workforce \setminus C) \setminus A = \{Coop\} Thanks 2. The first three are right, but you never defined A and B, i had to guess The complement one is right The powerset question is right, but put {} around everything you wrote I believe the cartesian product one is wrong - try it again and remember that a cartesian product is a set containing ordered pairs. I don't know what the set Workforce is, but I can tell that your last answer is wrong; here is why: Let M = (Workforce / C), M cannot possibly contain anything in C, therefore it cannot contain Coop M/B cannot possibly contain anything not in M, and Coop is not in M, so M/B cannot contain Coop 3. ## Sets Hello Swift There's no problem asking for someone to proof-check your work. In fact it shows that you've had a good attempt yourself, and aren't just relying on others to do the work for you. One very important thing, though, is to copy the question as accurately as you can. Otherwise, we have to guess what you actually meant. I've added some comments in red to your work below, where you haven't been as accurate as you should be. I hope you find my comments helpful. Grandad Originally Posted by Swift Its me again, sorry. I was wondering would proof checking work be allowed in these forums rules as I have done the working out but was wondering would someone be able to go through it and just tell me which ones are wrong without telling me what the answer is so that I can go back too that question and attempt it again, as doing it myself teaches myself and someone giving me an answer is just pointless as it wont benefit me in anyway, agree? Anyway here is the key; Key \displaystyle Stores =$$\displaystyle \{Tesco, Lidl, Asda, Coop, Aldi \}$
$\displaystyle Department = $$\displaystyle \{Sales, HR, Management \} \displaystyle Place =$$\displaystyle \{Cardiff, Bristol \}$
$\displaystyle Teams = $$\displaystyle \{1, 2, 3 \} \displaystyle 1 = \displaystyle \{Tesco, Lidl \} I assume you mean A = {...} \displaystyle 2 =$$\displaystyle \{Aldi, Asda, Lidl \}$ ... and B = {...}
$\displaystyle 3 = $$\displaystyle \{Coop, Lidl, Aldi \} ... and C = {...} \displaystyle A\cup B\ = \{Tesco, Lidl, Aldi, Asda \} \displaystyle A\cup B\cup C\ = \{Tesco, Lidl, Aldi, Asda, Coop \} \displaystyle B\cap C\ = \{Aldi, Lidl \} \displaystyle Stores \setminus B = \{Tesco, Coop \} These are all OK, if you use A, B and C instead of 1, 2, 3. \displaystyle The power set (Department) = \{\} \{Sales\} \{HR\} \{Sales, HR\} \{Management\}$$\displaystyle \{Sales, Management\} \{HR, Management\} \{Sales, HR, Management\}$

Be careful to use the correct notation. The power set of a given set A is the set of all subsets of A, including (of course) the empty set and A itself. So it's a set of sets. So use {...} to surround the elements (which are themselves sets in this case) and separate the elements using comma's. So your answer should read:

{{}, {Sales}, {HR}, {Sales, HR}, ...}

Can you see the difference?

$\displaystyle The Cartesian Product - Department x Place =$$\displaystyle \{Sales, Cardiff\} \{Sales, Bristol\} \{HR, Cardiff\}$$\displaystyle \{HR, Bristiol\} \{Management, Cardiff\} \{Management, Bristol\}$

Again, you're not using the correct notation. The Cartesian Product AxB of two sets A and B is the set of ordered pairs of the form (a, b) where a is in A and b in B. So it's a set of ordered pairs. So, use (... , ...) to denote each ordered pair, and enclose all the ordered pairs in {...}, separating each ordered pair from its neighbour using a comma. Like this:

{(Sales, Cardiff), (Sales, Bristol), ...}

$\displaystyle (Workforce \setminus C) \setminus A = \{Coop\}$ I'm guessing that by Workforce you mean the set you've called Stores originally.

So Stores \ C = {Tesco, Asda} and therefore (Stores \ C) \ A = {Asda}

Thanks