Step 1 :The problem is asking us to subtract the set {1,2,...,10} from the set {1,5,8} and then determine whether the resulting set is a subset of the original set {1,5,8}.
Step 2 :In set theory, the subtraction (or difference) of two sets A and B, denoted by A - B, is the set of all elements of A that are not in B.
Step 3 :So, we need to subtract the set {1,2,...,10} from the set {1,5,8}. This will give us the set of all elements in {1,5,8} that are not in {1,2,...,10}.
Step 4 :Next, we need to check whether the resulting set is a subset of the original set {1,5,8}. A set A is a subset of a set B (denoted by A ⊆ B) if every element of A is also an element of B.
Step 5 :The resulting set after subtracting {1,2,...,10} from {1,5,8} is an empty set.
Step 6 :An empty set is a subset of any set, including the original set {1,5,8}. Therefore, the correct symbol to use is ⊆.
Step 7 :Final Answer: \(\boxed{\subseteq}\)