mark each statement true or false.

1) The set of positive integers is closed under addition, but not subtraction.

2) A function f:XY, where X and Y are both sets of size 1, must be one-to-one, onto, and invertible.

3) The main difference between proofs by ordinary induction and strong induction, is that for the inductive step of ordinary induction you only use the preceding step n to show n+1, whereas for strong induction you rely on knowing all preceding steps i, left parenthesis base space case less or equal than i (base case =< i =< n), to show n+1.

4) (n Choose n) = 1, for all n element of straight positive integer numbers

5) A minimum spanning tree on an undirected graph may contain a circuit.