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MATH370_PracticeFinal - Name CSUSM Math 370 Instr Dr Andr...

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Name: CSUSM Math 370 Instr: Dr. Andr´ e K¨undgen SAMPLE ONLY Final Exam Show work, explain your reasoning and clearly mark your answers. Please ask about anything that is unclear. Use back sides of pages for scratch and overflow work, but clearly indicate which is which! 1. Short answers questions. (24 pts) a) Prove that the product of two odd numbers is odd. b) Give the proper definition of the symmetric difference of two sets A, B . c) State the Binomial Theorem. (Don’t forget the hypothesis!) d) What does it mean for a function f : A B to be onto? (Your answer should use only symbols and no words.) e) Give a set A such that { 4 } ∈ A and { 4 } ⊆ A , or explain why such a set can’t exist. f) Determine the number of partitions of the set { 1 , 2 , 3 } . 2. Prove that 5 n - 1 is divisible by 4, for every natural number n . (10 pts) 3. Circle all the properties which R = { (1 , 2) , (2 , 4) , (3 , 4) , (1 , 4) , (5 , 7) , (6 , 7) } satisfies. (No proof needed) (10 pts) R is reflexive. R is irreflexive.
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