TU Wien:Discrete Mathematics VO (Gittenberger)/Written Exam 2023-01

1) Solve: x^2 = 1 (4), 3x=4 (5), 6x = 3 (9)

2) Prove (E,S) with |E| = n and S = {X subset E: |X| <= m} is a matroid

3) Show that for a set of distinct numbers A sub {1..15} of size 8, there always exist two numbers which sum up to 16

4) Prove if Z3/ (x^2 + x + 1) is a field, list all elements. Is x+1 a unit? If yes give its multiplicative inverse