Discrete Math Help (sad story)

[Chopkilla]

Homework Statement

1. Let x and y be positive integers and assume that xy is odd.
Prove the following statement using the method of proof by contradiction:

Both x and y are odd.

2. Let A, B and C be the following sets:

A = (x є N | x< 25) B=(x e N | x = 2m for some positive integer m)
C = (x є N | x = 3m for some positive integer m)

Find each of the following sets. In each case, list all of the elements of the set.

i) A – (B u C) ii)A n C

3) Let A = {0,1,2,3,4,{0,2,4},{1,3,5},6,8}
is the following statement true or false?
Explain your answer
(э x єA) (x < A)

4) let A={1,2,3,4,5} find the following set, listing all of it's elements
{s є P(A)| 3 < 151}

5 let A and B be sets. Prove the following statements
i) AnB<A ii) A<AUB

6) let A.B and C be sets. Consider the following implication:
If A< BUC then A - B<C.
prove this implication using the method of proof by contrapositive.

7) let A,B and C be sets. Prove that (A-B)-(A-C)= (AnC)-B

Homework Equations

The Attempt at a Solution

well i have been going to this class now for a month and have only been able to attend 2 classes just recently, my father has passed away and it has been very hard for me, i tried negotiating with my professor but he is very ignorant and cold hearted to care about my personal life, i have this due by tomorrow morning, i got it two days ago, and have not been able to catch up from my readings for the last assignment yet (which i failed... because i did not attend classes) i am constantly learning the stuff i have been given but can't seem to understand these few questions just yet, so if anyone could help me out.. i would greatly appreciate it... i believe i have figured out the first one.. which i will write my attempt..

1) x є N
y є N xy = odd
assume x and y are even then xy is even (10x20 = 200)
because an even number multiplied by a even number is even resulting in a even product.
xy is even buy xy cannot be even if xy is odd this is a contradiction there for x and y are odd there for this statement is true...

that's what i tried to make of it.. still trying to figure out the rest.. please if someone could help me out.. i understand if you do my work you may feel i won't understand it, but i will be studying this and learning it. not just pawning off the answers. just to clear my conscience
thanks in advance

 

[HallsofIvy]

I'm sorry that your father passed away.

However, the fact that you consider any person who does not do what you want them to do to be "ignorant" doesn't speak very well for you. I miss my mother and father every day of my life- and they've been dead for 12 years. Sorry to sound heartless but that's life. No one is required to care about your personal life.

You have posted the set question separately and I responded there- are you saying you do not know how to find the union and intersection of sets?

As far as the first problem is concerned, you say "assume x and y are even"
You are asked to prove "x and y are odd" by contradiction. The opposite of "x and y are odd" is "either x or y is even"- not that both are. What you really want is that the product of an even integer with any integer is even. Are you aware that a number is even if and only if it can be written as 2n for some integer n? Use that.