Question 1210202
Let's break down this problem step by step.

**1. Understand the Constraints**

* We are looking for subsets of the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.
* Each subset must have at least two elements.
* The sum of the two largest elements in each subset must be 4.

**2. Identify the Possible Pairs**

Since the sum of the two largest elements must be 4, the possible pairs of largest elements are:

* (0, 4)
* (1, 3)
* (2, 2)

**3. Analyze Each Pair**

* **Pair (0, 4):**
    * The subset must contain 0 and 4.
    * Other elements can be any subset of {}.
    * There is only one subset: {0, 4}.

* **Pair (1, 3):**
    * The subset must contain 1 and 3.
    * Other elements can be any subset of {0}.
    * Possible subsets: {1, 3}, {0, 1, 3}.
    * There are 2 subsets.

* **Pair (2, 2):**
    * The subset must contain 2.
    * Other elements can be any subset of {0, 1}.
    * Possible subsets: {2, 2} which is just {2}, {0, 2}, {1, 2}, {0, 1, 2}.
    * However, we need at least two elements, so we must exclude {2}.
    * Possible subsets: {0, 2}, {1, 2}, {0, 1, 2}.
    * There are 3 subsets.

**4. Count the Subsets**

* For (0, 4): 1 subset
* For (1, 3): 2 subsets
* For (2, 2): 3 subsets

Total number of subsets = 1 + 2 + 3 = 6

**Therefore, there are 6 subsets of {0, 1, ..., 9} that have the property that there are at least two elements and the sum of the two largest elements is 4.**