Homework

A list of homeworks will appear here as they are assigned:

Submit your work on Gradescope after completion. Be sure to assign pages!

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Typesetting

You are not required to typeset your homework solutions; however, it is an easy way to improve the legibility of your documents. Many Allen School students learned to typeset in this course.

\(\LaTeX\) is the standard tool for typesetting mathematical materials. While it takes some time to learn, it will likely pay for itself in the long run. You can even use \(\LaTeX\) in places like Ed and Facebook Messenger!

These resources may be helpful for you to get started with \(\LaTeX\), with thanks to Adam Blank:

• A homework template that you can use. Here is a preview of the rendered result.
• A How to \(\LaTeX\) tutorial, including specific information on how to use the template.

If you have a CSE email address, you can also claim a free Overleaf Professional account. Overleaf is an online editor that spares you from having to install \(\LaTeX\) locally.

Guidelines

Inference Rules

• You may apply any other rule from the propositional logic reference sheet.
• You may apply commutativity, associativity, and double negation as many times as you want within a single step, provided you include that name in your rule. You may also combine these with other propositional logic rules, provided they are listed with the rule name.
• But you still must have a prior step in the correct order to “Eliminate \(\vee\)”
• Include line numbers for the referenced step, but for rules with multiple numbers do not worry about the ordering.
• Abbreviated rule names (like “MP” for “Modus Ponens”, or “Intro” for “Introduce”) are acceptable as long as they are clear.
• Remember to indent and change numbering style when starting a subproof.
• You may introduce variables as arbitrary with a separate step (provided they are truly arbitrary), but it is not required if it is a fresh variable introduced from eliminating a \(\forall\).

Symbolic Proofs

Symbolic proofs are part of the “training wheels phase” of proof writing. Follow these rules when you write your first symbolic proofs:

• Apply only one rule per step, and label each step with the name of the rule you applied.
• Respect order of operations. Operations are applied in precedence order, going from left to right across an expression. Be careful that you aren’t violating “implied” parentheses.
• Make sure you are applying the rule exactly as stated in the handout. The handout rules apply to compound propositions, as long as order of operations allow their application.

Homework in General

We evaluate your work using these guiding principles:

• Legibility. You may lose points for solutions that are not legible. We cannot award points for solutions that we cannot easily read. Please consider typesetting!
• Clarity. Remember to be mathematically formal and jot down your thoughts and assumptions. A proof is seldom strictly right or wrong; instead, it is only as convincing as the extent your human reader is convinced.
• Style. This can be subjective, but it mostly boils down to organizing your work to make it easy to follow. Make sure you set up consistent notations beforehand, communicate information concisely (unlike this), and give your work a good proofread from start to finish.

You can submit a regrade request on individual problems after we release feedback. Regrades will be open for a week.

We will not debate the amount of points deducted for mistakes. Those are entirely at the discretion of the course staff.