Math 291 Lab 5 Due Monday February 19, 2018

Instructions: Use L^{A}TEX to typeset a document containing each component described below. Turn in your lab by emailing it to fagerstrom@mnstate.edu. You should email both your raw TEX (.tex) file and your compiled document (in either .dvi or .ps or .pdf form).

You will be graded on both your raw TEX code and the accuracy of your compiled document. Name your file in the format of JaneDoeLab2.tex Include a name block similar to the one described in Lab 1 Set up your page using \setlength{\topmargin}{0in}, \setlength{\textheight}{9.5in}, \setlength{\oddsidemargin}{-.75in}, \setlength{\textwidth}{7.5in}.

1. Typeset the following table.

p q ¬p ¬p ∨ q p ∨ q ¬(p ∨ q)
T T F  T  T  F
T F F  F  T  F
F T T  T  T  F
F F T  T  F  T
↑  ↑

2. Typeset the following matrices or determinants, using the matrix shortcuts in the appropriate package.

(a) [\begin{matrix}3 & 7 \\ 2 & 1 \end{matrix}]

(b) |\begin{matrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}|

(c) \begin{cases}⊙ & ⊕ \\ ⊗ & ÷ \end{cases}\}
(d) (\begin{matrix}α & β & γ \\ δ & ϵ & ζ \end{matrix})
(e) ∥\begin{matrix}e^{x} & e^{−x} \\ e^{−x} & e^{x} \end{matrix}∥

3. Typeset the following sentence:

This is a silly little matrix ( \begin{matrix}♡ & ♠ \\ ♢ & ♣ \end{matrix} ) that includes the suits from a deck of cards, and I note that the black suits are black, although the red suits are not red.

4. Use the cases command from the amsmath package (look it up) to type the following sentence (make sure to include the period that ends the sentence in the appropriate place).

The function is defined by f(x) = \begin{cases}3x − 5 & if x > 4 \\ 5 − x^{2} & if x ≤ 4 \end{cases}.

5. Type three parboxes in a line, each of the same width, with one or two words before the first box, another one or two words in between the first two boxes, another one or two words between the second and third boxes, and finally at least one word after the last box. Choose the width of your parboxes to keep it short enough that it fits on one line. Fill your boxes with word phrases that are at least four lines (within the box) long. Make the first box stick up over the outer line of text, the middle box hang down from the outer line of text, and the last box be centered with the outer line of text.

I don’t care what your text is, as long as it is appropriate for polite conversation.

6. Create a table with one row and four columns, using the appropriate commands in the tabular environment to create a box around your entire table, vertical bars between columns 1 and 2 and between columns 3 and 4, and a double vertical bar between columns 2 and 3. For each of the four entries in your column, create a minipage containing the same five-word sentence (you choose the sentence, as long as it is appropriate for polite conversation). Set the widths of your four minipages to be 0.5 cm, 1 cm, 2 cm, and 4 cm, respectively.