(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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. Relevant 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

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Discrete Math Help (sad story)

**Physics Forums | Science Articles, Homework Help, Discussion**