Homework Set 1

Submitting Your Work

Your work must be submitted to Anchor for degree credit and to Gradescope for grading.

For any work completed outside of GitHub or Gradescope:

  1. Typeset your work in LaTeX.
  • You should use \begin{enumerate} to create a numbered list, and your solutions to each problem should match with the corresponding number on the assignment.
  • For example, if an assignment has 10 numbered problems, your enumerate should have 10 \item commands, with your solution(s) to problem 1 under the first \item, problem 2 under the second and so on.
  • If you skip a problem, just leave the \item blank, otherwise the numbers of your solutions will not match the assignment document. Here is an example Overleaf document showcasing this format.
  1. Compile into a PDF. This can be done easily through an Overleaf account, otherwise you will need to install LaTeX.
  2. Submit the pdf to Gradescope via the appropriate submission link for the course.
  3. Upload the pdf to Anchor using the form below.

Note: Anchor submissions can occur at any time during the term, but it is critical that you upload all of your work to Anchor before the last day of the term. Gradescope submissions must be submitted before the deadline (or the late deadline, if applicable).

It is required that all assignments are submitted as a PDF generated from a LaTeX document.

Assignments submitted in any other form will earn zero credit.

  1. [5 points] Why do we pronounce the X in LaTeX differently than one might expect in English?

  2. [10 points] Add an XKCD comic to your document. You should add the comic as an image, and add a link to the XKCD site to credit the creators. The link should be clickable in the final PDF.

  3. [10 points] If you had a truth table in a CSV file, and wished to transfer it into LaTeX, would you re-write it by hand or create a program that would typeset the table for you? If you would re-write it, explain why. If you would create a program, write some pseudocode.

  4. [5 points] Create an example of each of the following in LaTeX: A fraction, an exponent, the greek letter $\sigma$ (sigma), uppercase $\Sigma$ (sigma), and an expression with at least two variables.

  5. [10 points] Create a truth table for the following expression: $\neg (p \vee q) \wedge r$.

  6. [10 points] Show that the following expressions are equivalent:

$$(p \vee q) \rightarrow \neg r$$

$$\neg r \vee (\neg p \wedge \neg q)$$

  1. [10 points] Use a subset proof to show that $(A \cap B) \cup (B \cap C) \equiv B \cap (A \cup C)$.

  2. [10 points] Write the following in mathematical notation: Set A contains ordered pairs of integers such that these pairs add to 10 or multiply to 16.

  3. [10 points] Give an example of an equivalence relation, and prove that it is an equivalence relation.

  4. [10 points] Create an Antisymmetric relation on ${1,4,9,16,25}$.

  5. [10 points] If a relation is not reflexive, does that mean it is irreflexive? If this is true, prove it. If it is false, provide a counterexample.