- Chapter 1:
Problem 1. Let *A*be the set of (straight) lines on a plane. Consider a relation*R*such that*xRy*when lines*x*and*y*both contain point (0,0). Explain why*R*is not an equivalence relation.Problem 2. Show that the lexicographical ordering is transitive. (This is a part of the proof that this relation actually is a strict total order.) Problems 1.7, 1.8 from the lecture notes Deadline: Saturday 23/10 for at least 2 (out of 4) problems. - Chapter 2:
Problem 2.1: Problem 2.2 from the lecture notes. It is sufficient to consider it for the case of A of 6 elements, or the case of A infinite. Problem 2.2: Consider the poset of the first diagram of problem 2.1 from the lecture notes. Show that it is a lattice. Show that the lattice is not distributive. (Begin with naming the poset's elements.) Alternatively, the same for the poset (P,â‰¤), where P={0,1,a,b,c}, 0â‰¤{a,b,c}â‰¤1, and a,b,c are incomparable.Problem 2.3: Problem 2.12 from the lecture notes, without (3). Deadline: 30/10 for 2.1, 4/11 for 2.2 and 2.3 - Chapter 3: problems
here
(extended on 11/11).
- Chapter 4:
Problem 4.1. Explain what is wrong in this erroneous inductive proof. Begin with making it clear which induction principle is used. (Deadline: as soon as possible:) Problems 4.2, 4.3 - Chapter 5: the problems here; deadline - 7/12.
- Chapter 6: the problems here (except for those possibly solved at a lecture); deadline 15/12
. It is absolutely
not allowed to copy or rephrase each others solutions, or to solve the exercises jointly Solutions handed in after the deadline will be dealt with a low priority, thus graded possibly rather late. |

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Last updated: 2021-12-15