Quiz 1

Milestones

Rubric

All questions on the quizzes in this course are out of 3 points. When assessing these quizzes, score answers as follows:

• 3 is reserved for excellent responses that that fully explain the answer to the question, show a true understanding of the question being asked, and don’t contain any errors. As a general guideline, we expect no more than 25-30% of answers are likely to receive a 3 on any particular question.
• 2 is awarded for a good response that’s getting at the right idea, but might not explain it fully or might have a few minor errors. 2, indeed, is what the course expects most students are likely to earn. As a general guideline, we expect approximately 50-60% of answers are likely to receive a 2 on any particular question.
• 1 is awarded for an inadequate response that misses the mark, is wholly incorrect, or otherwise fails to answer what the question is asking.
• 0 is given to answers that are exceedingly brief, or blank, and as such are effectively non-responses.

The above rubric should be applied for all questions on the quiz.

If you give a score lower than full credit, please include a brief comment in the “Provide comments specific to this submission” section of the form. You can also re-use comments in the “Apply Previously Used Comments” to save time so that you don’t find yourself typing the same thing over and over!

Grading Responsibilities

Answer Key

Question 1

1. No. Sentence 1 can be true while Sentence 2 is false in a world where neither Hermione nor Harry are in the library.
2. Yes. If we know that Harry is in the library, then Sentence 1 is true regardless of whether Hermione is in the library or not. Therefore, in every world where Sentence 2 is true, Sentence 1 is also true.
3. Yes. Sentence 3 a logical contradiction — there are no worlds where it holds true. Therefore, by the definition of entailment, anything can be entailed.
4. Yes. This is an application of logical resolution, where we eliminate the complementary literals “Harry is in the library” and “Harry is not in the library.”

Question 2

1. (A ∨ B) ∧ ¬(A ∧ B) or, equivalently (A ∧ ¬ B) ∨ (¬ A ∧ B)
2. The sentence would hold true when A and B are both the same value: either both false or both true.

Question 3

1. R → (C ∧ ¬ S)
2. (¬ R ∨ C) ∧ (¬ R ∨ ¬ S)

Question 4

1. Hermione is a student enrolled in Charms.
2. There is a student who is enrolled in Potions.
3. Everyone who is a student is not enrolled in Charms.
4. There is a course that both Harry and Ron are both enrolled in.