How many onto (or surjective) functions are there from an n-element (n => 2) set to a 2-element set?

Related MCQs

• Let A be a finite set. If f : A → A is injective then it is surjective.
• If A is a set with 3 elements, how many equivalence relations are there on A? Hint: The set of equivalence classes for a given equivalence relation on A is a partition of the set A.
• How many relations are there on a set with n elements that are symmetric and a set with n elements that are reflexive and symmetric?
• The number of functions from an m element set to an n element set is:
• Let f : X →Y and g : Y → Z. Let h = go f : X → Z. Suppose g is one-to-one and onto. Which of the following is FALSE?
• Pigeon Hole Principle says that if there are many pigeons and a few pigeon holes, then there must be some pigeon holes occupied by--------------
• In a room containing 28 females, there are 18 females who speak English, 15 females speak french and 22 speak german. 9 females speak both english and french, 11 females speak both french and german where as 13 speak both german and english. How many females speak all 3 languages?
• In a group of athletic teams in a certain institute, 21 are in the basket ball team, 26 in the hockey team, 29 in the foot ball team. If 14 play hockey and basketball, 12 play foot ball and basket ball, 15 play hockey and foot ball, 8 play all the three games. (i) How many players are there in all?
• Let S = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21}. What is the smallest integer N > 0 such that for any set of N integers, chosen from S, there must be two distinct integers that divide each other? IZ
• Let f: A → B and g: B→C be functions where A = {1, 2, 3, 4}, B = {1, 2, 3, 4, 5}, and C = {1, 2, 3, 4, 5, 6}, f = {(1, 2), (2, 3), (3, 2), (4, 5)} and g = {(1, 3), (2, 4), (3, 5), (4, 6), (5, 1)}. Find g o.f (2).