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Hard

December 15th

Questions

What is the cardinality of the set of all subsets of a set with n elements?

What is the cardinality of the set of all functions from a set with m elements to a set with n elements?

What is the number of non-similar connected graphs with n vertices?

What is the number of non-similar labeled trees with n vertices?

What is the number of ways to partition a set with n elements into non-empty subsets?

Medium

August 6th

Questions

What is the symbol used to represent the empty set in set theory?

In combinatorics, what is the number of ways to arrange n objects in a row?

What is the sum of the interior angles of a triangle?

What is the Pythagorean theorem used to calculate?