Problem B. Recall that a order relation is a well-ordering, if every nonempty set has a smallest element. Determine which of the following linear orders is a well-ordering I. The lexicographical order on Z × Z; 2. The lexicographical order on Z>0 × Z〉 0

#20

3. Let X be a set, and let 1 and 2 be two binary relations on X. Define the lexicographic binary relation as follows: for any z, y € X, we have x ɩ if and only if at least one of the following two conditions holds:¹. • ï >1 Y • ~₁ y and r₂ y. [If 1 and 2 capture how a decision maker feels about different aspects of a decision, then is one way of combining them: use aspect 1 to make decisions, but if aspect 1 does not make the decision easy, then use aspect 2 to break ties.] Explain why each of the following is true: (a) If x, y € X have r L y, then r i y. (b) is complete if both ₁ and ₂ are complete. AL (c) is transitive if both ₁ and ₂ are transitive. [Hint: part (a) of this question and parts (b,c) of the previous question may be helpful.] is a preference relation if both ₁ and 2 are preference relations. 2 is exactly 1, then is exactly ı. L (d) (e) If (f) If 2 is exactly 1 (see question 2(a)), then is exactly ₁.

Let A = {3, 4, 5} and B = {5, 6, 7}, and let S be the "divides" relation from A to B. That is, for every ordered pair (x, y) E Ax B, x Sy x|y. Which ordered pairs are in S and which are in S-? (Enter your answers in set-roster notation.) {1} S = %3D S-1

Discrete Math

DISCRETE MATHEMATICS​​​​​​​

2. Let A = {0,2,4, 6,8} and B = {1,3,5,7} have universal set U = {0,1,2,...,8}. Find: (a) Ā (b) В (d) AUĀ (g) ĀnĒ (h) AnB (е) А -А (c) AnĀ (f) AUB (i) AxB

I am having trouble working thru this problem, any help would be appreciated.