aditikedia wrote:Can someone explain this?
Statement 2 could be true in the following situation too:
--->The terms in the set could be (-2, 2, -3, 3) The sum of all these terms will still be 0. Nowhere does it say that the terms are positive.
Therefore how is statement 2 sufficient?
Statement 2 does not say that the sum of
all numbers in the set will be zero. It says that the sum of
any two numbers in the set will be zero. The set cannot be {-2, 2, -3, 3} because, for example, 2+3 is not zero.
Returning to the question,
If there are more than 2 numbers in a list, is each number in the list equal to 0??
(1) The product of any two numbers in the list is equal to 0
(2) The sum of any two integers in the list is equal to 0
From 1), any list with exactly one nonzero element will satisfy this condition. For example, if you multiply any two numbers in this list:
0,0,0,0,100
you will get zero.
From 2), if we have a list that begins:
a, b, c...
we know that a+b = 0, so a = -b. We know that b+c = 0, so c = -b. So our list must begin:
-b, b, -b, ...
But the sum of the first and last numbers above must be equal to zero:
-b + (-b) = 0
-2b = 0
b = 0
So the first three numbers in our list must be zero, and if there is another number d in our list, it must be true that d+0 = 0, so d=0.
