Answer:
a) must be met
Step-by-step explanation:
We have two conditions:
a) For every and , there exists , such that .
b) There exists and such that .
We will prove that conditon a) is equivalent to
If a) is not satisfied, then it would exist and such that, for every , . This implies that is a lower bound for A and in consequence
Then, implies a).
If is not satisfied then, and in consequence exists such that . Then and, for every ,
.
So, a) is not satisfied.
In conclusion, a) is equivalent to
Finally, observe that condition b) is not an appropiate condition to determine if or not. For example:
- <u>A={0}, B={1}</u>. b) is satisfied and
- <u>A={0}. B={-1,1}</u>. b) is satisfied and