Let , define
where "count" denote the number of elements in that set.
Let M be the set of all even numbers, N be the set of all odd numbers, and P be the set of all perfect squares.
Q2: If A and B are disjoint sets, show that
Q3: Is it a measure?
My solutions so far:
Q1: For , and I have since only half of those will be even, so the whole limit would equal to , same goes for all odd numbers.
For the perfect squares, should it be ?
And if I can prove Q2, doesn't that automatically prove Q3?