MATH 2030 Quiz: MATH 2030 University of Manitoba Quiz 6

• School: University of Manitoba
• Department: Mathematics
• Course: MATH 2030
• Professor: All

Document Summary

Instructor: r. craigen: time: 20 minutes no aids permitted, total marks: 20. Student number: consider the following relation on x = {1, 2, 3, 4}: {(1, 1), (2, 2), (3, 3), (4, 4), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)} [2] (a) draw the digraph for (x, r) [2] (b) give reasons why (x, r) is a partial order. [2] (c) show two distinct linearizations of this partial order (as lists of the elements) [2] (d) draw the hasse diagram for (x, r) [2] (e) give a reason why (x, r) is not a lattice. There is no maximum element; lattices always have a unique maximum. There is no least upper bound for 1,2. Since (x, r) is re exive it is not strict: for the following hasse diagram of a strict partial order: [4] (a) demonstrate the conclusion of mirsky"s theorem by listing an appropriate chain and corresponding an- tichains. f c j.