SOLUTION: For all numbers x and y, let the operation * be defined by x * y = x - y. If a and b are positive integers, which of the following can be equal to zero? I. a * b II. (a + b) * b

Question 337060: For all numbers x and y, let the operation * be defined by x * y = x - y. If a and b are positive integers, which of the following can be equal to zero?
I. a * b
II. (a + b) * b
III. a * (a + b)
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I and III

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Since x * y = x-y, this means that a*b = a-b. So if a=b, then a*b=a-b=a-a=0. So (I) is true.

So because x * y = x-y, we can also say that (a+b)*b = (a+b)-b = a. But if 'a' is a is a positive integer, then 'a' is NOT zero. So (II) is NOT true.

In a similar (but slightly different) fashion, (III) is also false using the same reasoning above.

So only (I) is true.

So the answer is A)

If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my website.

Jim
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