1. State whether the following quantified formulate are true over the natural numbers N={1,2,...}

(1) xyz [xy^2 z^2]

(2) xyz[(x=y^2) (x=z^2)]

(3)uvwx [(w=u+v) (x^2=w^2+1)

give your reasons in each case

2. use mathematical induction on n to prove that (2n)!/2^n is a natural number for all n >=0.

(In other words, 2^n divides (2n)! for all n>=0)

3.Exhibit a language A over the alphabet {a,b} such that lAl = 5 and lA^2l = 11

(Note that A^2 = AA.)