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# Exam1 - CSE 5211 Fall 2008 Exam 1 Points 40 Time 85 min 1a...

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CSE 5211 Fall 2008 Exam 1 Points: 40 Time: 85 min 1a. Prove by induction that the number of arcs on a tree with n nodes is n -1. [2] 1b. Prove by induction that [2] 1+2+3+ … n = n(n+1)/2 1c. What is the cardinality of the set that you can form out of the subsets of a set with n elements? E.g., if the set is {a, b}, its subsets are {}, {a}, {b}, {a,b}, and the asked set is { {{}}, {{a}}, {{b}}, {{a,b}}, {{a}, {b}}, {{a}, {a,b}}, {{b}, {a,b}}, {{a}, {b}, {a,b}} } . [1] 1d. With 10 points in space (not any three of them are collinear), how many triangles can you draw? [1] 1e. Find a satisfying variable assignment (a=?, b=?, c=?) for the following CNF formula: (-a V b) ^ (b V c) ^ (-b), Where a, b and c are Boolean variables, –a indicates negation of a , V indicates ‘or’, and ^ indicates ‘and’. [1] 1f. Depth of a single-node tree is 0, and the depth of any node is the depth of its parent plus 1. Height of a tree is the maximum depth over all the nodes in the tree. Branching factor of a balanced tree is the number of children of any node, except that of the leaves. Draw a tree with the branching factor 3 and depth 3. What is the total number of nodes of

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Exam1 - CSE 5211 Fall 2008 Exam 1 Points 40 Time 85 min 1a...

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