TU Wien:Discrete Mathematics VO (Gittenberger)/Written Exam 2022-01-26

1.) Calculate the number of spanning forests of a given graph.

2.) {a,b}* = {a}* x ({b} x {b}* x {a} x {a}*)* x {b}* Explain why this equality holds. Furthermore state the generating function counting all elements made of {a,b} which contain neither aaa nor bbb.

3.) 4x=2(mod 11), x^2=1(mod 6), 12x=8(mod 20)

4.) R=Z_5[x]/(x^2+3x+1) List all elements of R. Is R a field? Is x+3 a unit in R?