Integers a,b,c

It's E.

1. We have only + and * so we can safely say it doesn't matter if we swap places or no.

2. Is obvious

3. As 1 we can safely say we can do this since with + and with * we can do this kinds of swapping.

1+2+3=2+3+1

1*2*3=2*3*1

If we had - or / somewhere on the other hand.. but we don't.

1st I did this the long way btw.

a+b-ab+c-ca-cb+cab=a+b+c-bc-ab-ac+cab before I realized we are dealing only with + and *. And with + and - we can swap all we want.

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gaggleofgirls: Master | Next Rank: 500 Posts; Posts: 138; Joined: Thu Jan 15, 2009 7:52 am; Location: Steamboat Springs, CO; Thanked: 15 times

by gaggleofgirls » Mon Jan 26, 2009 8:37 am

i just did out the math...

I = b@a = b + a -ba, which is the same as a + b -ab

II = a@0 = a + 0 - a*0 = a + 0 - 0 = a

III for (a@b) @ c you get:
a + b -ab + c - ca - cb - cab

For a @ (c @ b) you get:
a + b + c -bc - ab - ac + abc

Then just cross out the matching values and you realize that they all cross out, hence equal.

So I II and III are all true.

Answer is E.

-Carrie