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**1. 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

**2. Homework Equations**

**3. 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 beleive 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