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- An operation $∗$ on the set of positive integers is defined by $a ∗ b = (a + b)^{a−b}$ . Evaluate:
- If $U$ is a universal set such that $ \forall A,B \in U$ then is it true that $A \backslash B = A \cap B^c$ ?
- If $U$ is a universal set such that $ \forall A,B \in U$ then is it true that $A \cup (A \cap B) = A $ and $A \cap (A \cup B) = A $ ?
- If $U$ is a universal set such that $A,B \in U$ then is it true that $A\cup (B \cap C )= (A \cup B) \cap (A \cup C)$ and $A\cap (B \cup C )= (A \cap B) \cup (A \cap C)$
- If $U$ is a universal set such that $A,B \in U$ then is it true that $(A\cup B) \cup C = A \cup (B \cup C)$ and $(A\cap B) \cap C = A \cap (B \cap C)$

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