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)

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!!!