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.

Q1: Find

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?

Thank you!