# proves -discrete math !!! please help!!!

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• Oct 14th 2008, 02:39 PM
olenka
proves -discrete math !!! please help!!!
1. Prove: for all a ϵ Z, for all b ϵ Z if a│b then aČ│bČ

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

Please help!!!!(Headbang)
• Oct 15th 2008, 11:29 AM
Moo
Hello,
Quote:

Originally Posted by olenka
1. Prove: for all a ϵ Z, for all b ϵ Z if a│b then aČ│bČ

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

Quote:

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

Quote:

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 ? (Surprised)
• Oct 15th 2008, 02:48 PM
olenka
ehhhh ....help
Quote:

Originally Posted by Moo
Hello,

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

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

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

This may be all you need eh ? (Surprised)

Hi, thanks for that , but could U be more specific...and show me exactly step by step process of solving that problems??? (Itwasntme) Thanks!!
• Oct 18th 2008, 11:43 PM
Moo
Quote:

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??? (Itwasntme) Thanks!!

Yo,

What don't you understand exactly ? Have you at least tried to do them ? (Doh)
• Oct 20th 2008, 07:40 PM
olenka
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 aČ│bČ

We say a divides b denoted by ahttp://www.mathhelpforum.com/math-he...c9a8ca95-1.gifb if there exist a k such that b=ak kεZ by definition of divides. then http://www.mathhelpforum.com/math-he...942f683e-1.gif, so http://www.mathhelpforum.com/math-he...a9af6a86-1.gif, therefore, http://www.mathhelpforum.com/math-he...e7086139-1.gif
by closure property of multiplication. Since m is an integer, then mb^2 is an integer. Thus,aČ is expressed as m times b square, so by def of divides aČ│bČ . So by real number properties for all integers a and b ϵ Z if a│b then aČ│bČ.

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