Evaluate the truthfulness of the following set theory statements: 1. A - B ⊆ A 2. B - A ⊆ B 3. If A = B, then A + B = ∅ 4. A - B ≠ B - A

Here are the evaluations of the given set theory statements: 1. Statement: A - B A Explanation: The set A - B (also written as A B) contains all elements that are in set A but not in set B. By definition, every element in A - B must be an element of A. Therefore, A - B is a subset of A. Truth Value: True 2. Statement: B - A B Explanation: Similarly, the set B - A contains all elements that are in set B but not in set A. Every element in B - A must be an element of B. Therefore, B - A is a subset of B. Truth Value: True 3. Statement: If A = B, then A + B = Explanation: Assuming A+B denotes the symmetric difference* A B = (A B) (B A). If A = B, then A B = (since all elements of A are also in B) and B A = (since all elements of B are also in A). Therefore, A B = = . Truth Value: True 4. Statement: A - B ≠ B - A Explanation: This statement claims that A - B is always* not equal to B - A. This is not universally true. For example, if A = \1\ and B = \1\, then A - B = and B - A = . In this case, A - B = B - A. Since we found a counterexample, the statement is false. Truth Value: False 5. Statement: A - B = A - (A B) Explanation: The set A - B contains elements in A but not in B. The set A - (A B) contains elements in A but not in the intersection of A and B. An element x is in A and not in B if and only if x is in A and x is not in (A B). This is a fundamental identity in set theory. Truth Value: True 6. Statement: A - = A, A - A = Explanation: This statement consists of two parts: A - = A: The set A - contains elements in A that are not in the empty set