Urban population between n and m is the number of members of the club each club the number of members of both clubs even prove m <n

To prove that m < n, where m is the number of members in one club and n is the number of members in another club, given that the number of members of both clubs is even, we can use a proof by contradiction.

Assume that m >= n, so m is greater than or equal to n.

Since the number of members of both clubs is even, we can represent the number of members of both clubs as 2k, where k is a positive integer.

From the given information, we know that the urban population between n and m is the number of members of the club.

So, the number of members between n and m can be represented as m - n.

Since we assumed m >= n, we have m - n >= 0.

The number m - n is the urban population between n and m.

Since the urban population is the number of members of the club, m - n should also be even.

However, if m - n >= 0 and even, it means that it can be represented as 2k, where k is a positive integer.

Therefore, we have m - n = 2k.

Rearranging the equation, we get m = 2k + n.

Since m = 2k + n, and we assumed m >= n, this implies that m >= 2k + n.

But this contradicts our assumption that m >= n.

Therefore, our initial assumption m >= n must be false.

Hence, the only valid conclusion is that m < n.