If the operation * is defined for all integers a and b by a*b = a+b-ab, which of the following statements must be true for all integers a,b and c ?
1. a*b = b*a
2. a*0 = a
3. (a*b)*c = a*(b*c)
- 1 only
- 2 only
- 1 and 2 only
- 1 and 3 only
- 1,2 and 3
This problem is listed here somewherez.
I: a+b-ab= b+a-ba OK
II: a+0-(a)0=0+a-0(a) OK same thing
III: is def intimidating. just work it like the functions in the MGMAT book
if you have that:
a+b-ab*c --> (a+b-ab+c)-(a+b-ab)c = (b+c-bc)+a - a(b+c-bc) --> a+b-ab+c-ac-bc-abc= b+c-bc+a-ab-ac-abc
a+b+c-ab-ac-bc-abc=a+b+c-ab-ac-bc-abc Everything cancels out! So suff.