Final answer:
If set a is a subset of set b (a ⊆ b), then the set difference a − b must be empty (ø) because there are no elements in a that are not already in b.
Step-by-step explanation:
To prove that if a ⊆ b, then a − b = ø, let’s begin by understanding what the symbols mean. The symbol ⊆ denotes 'is a subset of,' which means that every element in set a is also an element in set b. The expression a − b represents the set difference, containing elements that are in set a but not in set b. To prove the statement, assume that a ⊆ b. This implies that there can be no element in set a that is not in set b. Therefore, when we try to find a − b, there are no elements to include in this set, since all elements of a exist in b. Hence, the set difference a − b is empty, which is denoted by the empty set symbol ø.