# Errata - Applied Discrete Structures - V3.2

As significant mathematics errors appear, they will be logged here. Most of the typographical errors (missing/extraneous spaces, mathematics in non-math font, etc.) are not listed.

## Version 3.2 - January 2017

• Introduction, In Figure .0.6 (The 3-cube) there should not be an edge connecting 010 to 101. (Already fixed in the html version)
• Section 1.2, Problem 4, part (d): The equality $A \oplus (B\cap C) = (A \oplus B)\cap (A \oplus C)$ is not always true. For example, if $A = \{1\}$, $B = \{1\}$, and $C =\emptyset$, then the left hand side of the identity is $\{1\}$ while the right hand side is the empty set. Another example is $A = \{1,2\}$, $B = \{1\}$, and $C =\{2\}.$(found by Jim Propp)
• Section 3.8 The answer to exercise 1(a) should be $(\forall x)(F(x)\to C(x))$. (Found by Maksim Mints, UML Student)
• Section 5.1 The answer to exercise 1(e) should be $\left( \begin{array}{ccc} -12 & 7 & -7 \\ 21 & -6 & 6 \\ \end{array} \right)$
• Section 9.6, Problem 3(a) the solution that is given is incorrect. It should be 4, not 3, since the graph in this part is a $K_4$. (found by Jeremy Joubert, UML student)
• Section 12.1 The solution to part (b) of exercise 1 should be $x_1 = -3+0.5 x_3$
• Section 12.1 The solutions to parts (a) and (b) of exercise 3 are incorrect. They should be
1. $\{(1.2+5x_3, 2.6-4 x_3, 4.5) \mid x_3 \in \mathbb{R}\}$
2. The solution set is empty
(found by Elizabeth Mahoney, UML student)
• Section 13.5 The tables for meet and join on $B_2$ contain an error. The correct tables are $$\begin{array}{lr} \begin{array}{c|cc} \lor & 0 & 1 \\ \hline 0 & 0 & 1 \\ \bf{1} & 1 & 1 \\ \end{array} & \begin{array}{c|cc} \land & 0 & 1 \\ \hline 0 & 0 & 0 \\ \bf{1} & 0 & 1 \\ \end{array} \end{array}$$ (found by Cameron Bolduc, UML Student)

Errata for V2.0----Errata for V3.0