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Which of the following is not a valid expression? Assume x and y are integer variables.

For each positive integer k, let Ak = { x ∈ ℝ | 0  ≤  x  ≤ 1/k  }. Which of the following sets is equal to ?

The function f : ℝ ⟶ ℝ defined by f(x) = x3 + 3×2 – x + 7 is O(x4).

Which of these matrices is an adjacency matrix for K 1, 3 ?

For arbitrary positive integers a, b, q and r, if a = bq + r, then GCD(a, b) = GCD(b, r).

What topic in units 10-11 of the course material did you find the most interesting?

For arbitrary integers a, b, and c, with a ≠ 0, if a | (b c), then a | b or a | c.

Which of the following symbols can be used as part of an identifier?

Define S, a set of bit strings, recursively as follows. Initial Condition:  0 ∈ S Recursion: If m ∈ S then 1m ∈ S. Which of the following best describes set S?  

For all positive integers a, b, c, and m with c > 0 and m > 1, if a ≡  b(mod cm), then a ≡ (c b)(mod m).