the family set of{Ai,iEI}is a partition of A,
the family set of{Bj,jEJ}is a partition of B,
than prove {AixBj,iEI and jEJ}is a parititon of AxB.
thanks for your helps.
First we show that each cell is not empty.
Given because of partitions .
Does that prove the first requirement?
Now disjoint cells.
If then WHY?
WHY does mean that ?
Now can you explain how this shows that different cells are disjoint?
Now the covering property.
If . How are we sure of this?
This means that .
How does that show that ?