# CS 70 Reading Quiz -- Week 2, Sunday

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1. True or false: The two propositions

∃ x ∈ N . ∀ y ∈ N . P(x,y)
and
∀ y ∈ N . ∃ x ∈ N . P(x,y)
are equivalent, no matter what P(x,y) is.

If you think this is true, give a brief explanation. If you think this is false, give an example of P(x,y) for which the two propositions are not equivalent.

2. Suppose that we want to prove by induction on n that n3 + 2n ≤ n2 + 3n for every natural number n. Fill in the base case part of such a proof (just the base case, nothing else; don't worry about the induction step).

3. What did you find difficult or confusing about the reading or the lectures, and what would you most like to see explained better? If nothing was difficult or confusing, and you understand the material pretty well, tell us what you found most interesting. Please be as specific as possible.