It seems I spent a bit too much time drawing cats and mats and a bit too little time proofreading on Homework 1. I was just trying to write up a key, and it turns out that Part 3 is wrong in a startlingly large number of ways.

My suggestion: burn the copy of Homework 1 that I handed out (but only someplace safe), and download Homework 1 version 2.0 from the website.

If you choose to soldier on with the one I handed out, here are the things that need to be changed:

→Reverse the meanings of p and q.

Part 3: For convenience, let’s label the sentences The door is open as p and The cat is on the mat as q. Using these labels, sentence (c) could be restated as “p and q.”

→Change ¬p to ¬q.

In logic, we use the symbol ¬ to mean “it is not the case that.” Thus, sentence (e) could be restated (using the labels above and the symbol) as “¬q.” Similarly, the symbol ∧ corresponds to “and” (it looks a little bit like an “a”) and ∨ corresponds to “or” (it’s not “and”). The “if…then” relation (implication) is represented by →, so sentence (d) can be written as “p→q“.

→Change “sentence (b)” to “the sentence The door is not open“.

Question 3.3: Restate the sentence The door is not open under the line in symbols.

Great start to the semester! I guess it drives home the importance of reading the blog, but still I will try to proofread future homeworks a bit better.