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Assignment_1_Answer_Key

Assignment_1_Answer_Key - can write{x|(x є U(x{0,2,3,4,6...

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Assignment 1 Answer Key Assume the natural numbers include 0, you were not penalized if you assumed otherwise. 1) 0, 3 or 6 would be acceptable answers 2) {}, {0}, {0, 1, 2, 3, 4} or C would all be acceptable answers 3) This is actually the same as #2, so the same answers are acceptable. 4) { (0,0) } and {(0,0), (0,3) } are examples of acceptable answers. (0,0) is not because it is an element of a subset of BxB not a subset of BxB 5) 3 6) There are more elements in A than B, so this is impossible. 7) Example: A -> B { (0,0), (2,3), (4,3), (6,6) } 8) {2,4} 9) Universal set has not been defined, but if we consider U to be the universal set we
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Unformatted text preview: can write: {x| (x є U) /\ (x ? {0,2,3,4,6} ) } 10) { {}, {0}, {3}, {6}, {0,3}, {0,6}, (3,6}, {0,3,6} } 11) 10 (or 9 if you excluded 0 from the set of natural numbers) 12) The cardinality of the power set of a set of cardinality x is 2 x . Since {a} = 4, we calculate 2 4 = 16. 13) f(6) = 6 14) g(5) = 7 15) Basis: n = 0; 0 3 = 0 2 *(0+1) 2 /4 = 0. Thus the statement is true for the base case n=0. Hypothesis: P(s) = Induction: for n = s+1 = = = 16) Basis: n = 0; 0 (0+1) = 0 = . Thus the statement is true for the base case n=0. Hypothesis: P(s) = Induction: for n= s+1...
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