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shingalated
September 23rd, 2007, 11:33 PM
I have no idea how to do any of these:
1.) Prove that if a+b is odd, then a^3+b^3 is odd.
2.) Prove that the product of 3 even integers is divisible by 8.
3.) Prove that (AnB)' is a subset of A' u B'
Thanks guys, I know this isn't really where to ask for help, but my math friend Jesus is gone, and I need help.

Kingsley
September 23rd, 2007, 11:40 PM
For the first question, the sum is always odd if a is odd and b is even or vice versa.

ghantoos
September 23rd, 2007, 11:42 PM
1) if a+b is odd => a OR b must be odd.
If a is even a³ is even too,
and if b is odd then b³ is odd too.
=> a³+b³ is odd. hope it is clear.
(a proper demonstration would be to replace a by 2n and b by 2m+1, do the math, and it should fit! :) )
2) An even integer can be written as the product of 2 and x, x being anything(even or odd).
if you take 3 even integers, A, B and C:
A=2a, B=2b and C=2c
then A*B*C=2a*2b*2c=8*a*b*c
I did my math in french, so sorry if the math terms aren't right.

cheers,

ghantoos

arkara
September 23rd, 2007, 11:52 PM
ok man you have to make
a+b=2n+1
and you have to prove that
a^3+b^3 is 2k+1
ok i am pretty good at maths
i dont remember very well but there must be some things if
odd x odd = odd? or sth like that
count on it
make (a+b)^3 and see where it goes

EDIT: THIS IS WRONG!!! DO NOT TRY
I AM TOO OLD TO DO THAT.
I WAS TAUGHT THAT 8 YEARS AGO AND I DONTREMEMBER THEM I AM AT THE UNIVERSITY NOW

regomodo
September 24th, 2007, 12:00 AM
at least show boolean algebra at least. sheesh! (only joking)

if a.b=odd then
a+b=odd;
else a.b= even;

thinking about it. That was **** and totally wrong. I was mixing my last programming attempt (VHDL) with what makes sense. Maybe i should have define my i/o (bit_vector, integers, naturals, etc) i'm tipsy)

My dissertaion supervisor asked if my motorbike (suzuki DR125) was front or rear wheel drive. Need i say more!

bapoumba
September 24th, 2007, 12:07 AM
ubuntuforums are not the proper place to get your homework done. Closing the thread, sorry.