1. Prove: for all a ϵ Z, for all b ϵ Z if a│b then a²│b²

2. Prove: for all n ϵ Z, n is add if and only if n² is odd.

3. using the definition of equal sets and the definition of subset, prove this

form of DeMorgan's Law:____ _ _
If A and B are sets then AUB=A∩B

2. Hello,
Originally Posted by olenka
1. Prove: for all a ϵ Z, for all b ϵ Z if a│b then a²│b²
If a|b, then b=ka
square both sides =)

2. Prove: for all n ϵ Z, n is odd if and only if n² is odd.
If n is even, then n=2n' ---> n²=...
If n is odd, then n=2n'+1 ---> n²=...

3. using the definition of equal sets and the definition of subset, prove this

form of DeMorgan's Law:____ _ _
If A and B are sets then AUB=A∩B
$\displaystyle A \cap B \subseteq A \cup B$

This may be all you need eh ?

3. ## ehhhh ....help

Originally Posted by Moo
Hello,

If a|b, then b=ka
square both sides =)

If n is even, then n=2n' ---> n²=...
If n is odd, then n=2n'+1 ---> n²=...

$\displaystyle A \cap B \subseteq A \cup B$

This may be all you need eh ?
Hi, thanks for that , but could U be more specific...and show me exactly step by step process of solving that problems??? Thanks!!

4. Originally Posted by olenka
Hi, thanks for that , but could U be more specific...and show me exactly step by step process of solving that problems??? Thanks!!
Yo,

What don't you understand exactly ? Have you at least tried to do them ?

5. ## discrete math already done! please check if it's right!

1. Prove: for all a ϵ Z, for all b ϵ Z if a│b then a²│b²

We say a divides b denoted by ab if there exist a k such that b=ak kεZ by definition of divides. then , so , therefore,
by closure property of multiplication. Since m is an integer, then mb^2 is an integer. Thus,a² is expressed as m times b square, so by def of divides a²│b² . So by real number properties for all integers a and b ϵ Z if a│b then a²│b².

if there is an mistake anywhere...please correct me. Thank you so much!!!