## Discrete Mathematics, Spring 2019

#### Day/Time: MWF 2:30pm – 3:20pm

Location: Phillips 381

Syllabus: click here

Piazza: click here

### Homework:

**Assignment 1:**

Wednesday: Section 1.1, problems 1, 2, 5, 6, 10, 11, 12, 13

Friday: Section 1.1, problems 16, 18, 19, 20, 21, 22, 23, 24, 25, but only parts a), c), e), and g) for each problem (when they exist)

**Assignment 2:**

Monday: Section 1.1, problems 29 and 30; Section 1.3, problems 1ace, 3a, 4a, 5, 7ac, 8ac, 17a, 24, 25, 35, 36

(remarks: use truth tables for problems 24 and 25, as in Monday’s lecture)

Wednesday: Section 1.3, problems 11ace, 12ac, 15a, 16a, 20, 24, 25, 27

(remarks: for problems numbered 15 and higher, use the methods introduced in Wednesday’s lecture to deduce the equivalences from known ones)

Friday: Section 1.6, problems 1, 2, 3, 4

(remark: for problems 3 and 4, use the names of the “rules of inference” from the table in the book)

**Assignment 3:**

Wednesday: Section 1.6, problems 5, 6, 9bc, 10af, 11, 12

(remark: for these problems, you’ll need to use the “take-away” from our discussion in lecture today. I’ll start Friday’s lecture with an example, but it couldn’t hurt to start thinking about these problems now!)

Friday: Section 1.4, problems 1, 2, 3, 5bd, 6bef, 11df, 12e, 13d, 14d, 16d, (remark: we didn’t explicitly cover in lecture how to take the negation of a propositional function, as in 5d, but I hope it’s clear…just read it as “it is not the case that”!)

**Assignment 4:**

Monday: Section 1.4, problems 5ac, 6acd, 11e, 12d, 15d, 17b, 18c, 19d, 20a, 23b, 24c, 25ad, 28ad

Wednesday: Section 1.4, problems 32, 33; Section 1.5, problems: 1ac, 2ac, 3be, 6be, 9bdf, 10dfgh, 13cd, 14cd, 19ad, 20ad, 24b, 25b, 27ad, 28ad, 41, 42, 45, 46

Friday: Section 1.5, problems 31ad, 32ad, 36de, 37ad; Section 1.6, problems: 7, 8, 9ade, 10cde, 13bd, 14bc, 15ad, 16ad, 17, 18, 19a, 20a, 23, 24

**Assignment 5:**

Monday: No written homework, but be sure to review the definitions of the concepts defined in lecture on 2/4

Wednesday: Section 1.7, problems 1, 2, 4, 5, 6, 7, 10, 14

Friday: Section 1.7, problems 9, 13, 17, 18, 19, 20, 25, 26 (hint: for these last two, it will help to read Example 10 in the book!)

**Assignment 6:**

Monday: Section 1.7, problems 12, 27, 28, 29, 33, 34 (and study!)

Wednesday: Section 1.8, problems 4, 5, 6, 9 (and study!)

Friday: no homework!

**Assignment 7:**

Monday: Section 1.8, problems 10, 11, 13; Section 2.1, problems 1, 2, 7, 8, 9, 10

Wednesday: Section 2.1, problems 12, 19, 23ab, 27

Friday: Section 2.1, problems 29, 30, 32, 33, 34a, 37, 40; Section 2.2, problems 1, 2, 3, 4, 14, 27, 31

**Assignment 8:**

Monday: Section 2.2, problems 16, 17, 20, 23, 26, 32, 33, 52, 53, 54, 56, 57

Wednesday: Section 2.3, problems 1, 2, 4ab, 5d, 6ab, 7ab, 30abd, 31a, 32, 42, 43

Friday: Section 2.3, problems 10, 12, 44, 45, 46, 47

**Assignment 9:**

Monday: Section 2.3, problems 11, 13, 14, 15, 20, 21abd, 22, 23abd

Wednesday: Section 2.3, problems 33, 34, 36, 37

Friday: Enjoy break!

**Assignment 10:**

Monday: see the homework problems posted on Piazza

Wednesday: Section 4.1, problems 1, 2, 3, 5, 6, 7, 8, 12, 14abc, 24

Friday: Section 4.1, problems 21, 22, 26ab, 27ab, 32, 33, 34, 35, 43, 44, 45, 46

**Assignment 11:**

Monday: Section 4.1, problems 48 (“closure property” means that the addition operation takes two elements in Z/m to an element in Z/m), 50, 52 (here, “writing out the addition/multiplication tables” means finding the sum and product of all pairs of elements in Z/6)

Wednesday: Section 4.3, problems 1, 2, 12, 55

Friday: Section 4.3, problems 15, 24, 32cde, 33cef

**Assignment 12:**

Monday: Section 4.3, problems 41, 42, 43, 44 (here, a “linear combination of a and b” means an expression of the form sa+tb for integers s and t)

Wednesday: No homework

Friday: No homework

**Assignment 13:**

Monday: Section 5.1, problems 3, 5, 6, 10, 11, 38, 41, 49, 50, 51

Wednesday: Section 5.1, problem 64; Section 5.2, problems 4, 5ac, 25

Friday: Section 5.2, problems 12, 29, 30; Section 9.1, problems 1, 2a

**Assignment 14:**

Monday: Section 9.1, problems 3bdf, 4, 5, 6bdf, 7ad (but ignore “antisymmetric” for all of these, since we didn’t cover that concept); Section 9.5, problems 1bcd, 2

Wednesday: Section 9.5, problems 3abc, 9, 15, 16, 27, 28 (for the parts of problems 2 and 3 you’ve done), 35, 36, 41, 42, 44cde, 45abc (for these last four problems, you need the definition of a “partition” of a set A, which we introduced in lecture today, but didn’t refer to by this name. A partition of A consists of a collection of subsets A_i so that A is the union of the A_i, and so that if A_i isn’t equal to A_j, then their intersection is empty. See page 644 for more details.)

**Assignment 15:**

Monday: Section 6.1, problems 1, 4, 7, 8, 22, 29, 40, 45, 55, 57ab

Wednesday: Section 6.3, problems 13, 15, 19, 29, 33ab, 35

Friday: Section 6.4, problems 3, 5, 7, 9, 16, 21, 25, 26a