best way to solve this symbolism?

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best way to solve this symbolism?

by josh80 » Wed Dec 11, 2013 5:07 pm
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?

I. a#b = b#a
II. a#0 = a
III. (a#b)#c = a#(b#c)

- I only
- II only
- I and II only
- I and III only
- I, II and III only

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by ganeshrkamath » Wed Dec 11, 2013 9:34 pm
josh80 wrote: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?

I. a#b = b#a
II. a#0 = a
III. (a#b)#c = a#(b#c)

- I only
- II only
- I and II only
- I and III only
- I, II and III only
I. a#b = a+b-ab
= b+a-ba
= b#a
TRUE.

II. a#0 = a+0-(a*0)
= a
TRUE.

III. (a#b)#c = (a#b) + c - (a#b)c
= a + b - ab + c - (a+b-ab)c
= a + b - ab + c - ac - bc + abc
= a - ab - ac + abc + b + c - bc
= a - ab - ac + abc + b#c
= a - a(b+c-bc) + b#c
= a - a(b#c) + (b#c)
= a#(b#c)
TRUE.

Choose E

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