STAT 379 - Problem Set 4 Due Date: February 28th, 2024 Suppose sets S and T are such that card(S) = n and card(T) - m for some n, m E N. Answer the following questions: 1. Recall the power set of S (denoted P(S)) is the set of all possible subsets of S. Find card(P(S)). - 1 pt 2. Find card(SXT). - 1 pt 3. How many possible relations are definable between S and T. - 1/2 pt (Hint: recall the definition of what a relation is and refer to Question 1). 4. How many possible functions are there from S to T? - 1 pt 5. If n T to be surjective. - 1 pt (A rigorous mathematical proof is not needed, just an intuitive argument). 6. If n > m, explain whether or not it is possible for a function f. S -> T to be injective. - 1 pt (A rigorous mathematical proof is not needed, just an intuitive argument). 7. How many possible injective functions are there from S to T? - 1 pt (Hint: You will need to answer Question 6 correctly to answer this one) 8. Assume n - m. How many possible bijective functions are there from S to T? - 1/2 pt Search