早上，农叔叔的店里起初玩具车的数量多于玩具船。 下午，他卖掉了玩具车数量的 $\frac{1}{2}$ 和 6 只玩具船。他没有卖完所有的玩具船。 下面的每个陈述要么是正确的，要么是错误的，要么是根据所给信息无法判断的。对于每个陈述，在正确的列中打勾（$\checkmark$）。

陈述	正确	错误	无法确定
早上，农叔叔起初共有 13 辆玩具车和玩具船。
下午，农叔叔剩下的玩具车比玩具船多。
农叔叔剩下的玩具车和玩具船数量之间可能的最小差值是 5。

1. Establish the constraints for the number of toy cars and toy boats at first.

Let $C$ be the number of toy cars at first, and $B$ be the number of toy boats at first.
Given: $C > B$.
He sold $\frac{1}{2}$ of the toy cars, so $C$ must be an even number.
He sold 6 toy boats and did not sell all of them, so $B > 6$. Since $B$ is an integer, $B \ge 7$.
Since $C > B$ and $C$ is even, the minimum possible value for $C$ is 8.

2. Evaluate the first statement: 'In the morning, Uncle Nong had a total of 13 toy cars and toy boats at first.'

Total at first = $C + B$.
Minimum $B = 7$.
Minimum $C = 8$ (since $C > B$ and $C$ is even).
Minimum total = $8 + 7 = 15$.
Since the minimum total is 15, it is impossible for the total to be 13.
Therefore, the statement is False.

3. Evaluate the second statement: 'In the afternoon, Uncle Nong had more toy cars than toy boats left.'

Cars left = $\frac{1}{2}C$.
Boats left = $B - 6$.
We need to compare $\frac{1}{2}C$ and $B - 6$.
Case 1: Let $C = 8, B = 7$. Cars left = 4, Boats left = 1. Here, $4 > 1$ (More cars left).
Case 2: Let $C = 10, B = 9$. Cars left = 5, Boats left = 3. Here, $5 > 3$ (More cars left).
Case 3: Let $C = 20, B = 19$. Cars left = 10, Boats left = 13. Here, $10 < 13$ (More boats left).
Since it can be either way depending on the initial numbers, it is Not possible to tell.

4. Evaluate the third statement: 'The least possible difference between the number of toy cars and toy boats Uncle Nong had left was 5.'

Difference = $|\frac{1}{2}C - (B - 6)|$.
Let's try to find a case where the difference is less than 5.
From Case 2 above: $C = 10, B = 9$. Cars left = 5, Boats left = 3. Difference = $5 - 3 = 2$.
Since 2 is less than 5, the least possible difference is not 5 (it can be smaller, even 0 if $\frac{1}{2}C = B - 6$, e.g., $C = 14, B = 13$, cars left = 7, boats left = 7, difference = 0).
Therefore, the statement is False.