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2025/WI Discrete Structures I (CS-250-01 MTH-231-01)

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True or False:

ℝ is a countably infinite set.

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Let X = {1, 2, 4, 8, 16, …}

Which of the following correctly defines X?

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True or False:

(1, 2) is equal to (2, 1)

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Let X be the statement: if A then B.

Let Y be the statement: if B then A.

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Let n be any integer, X the statement "n + 3 > 0" and Y the statement "n > 0".
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Let S be a space, x ∈ S, and P a probability distribution on S. If P(x) = 1, then we would call x...

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Let P(n) be a statement where n stands for a natural number. In a proof by induction of P, the base case proves P(k) where k is...

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From a set (not a multi-set) of 3 digits, how many unique 3 digit numbers can be created?

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Let f(n)  g(n) mean that f(n) = o(g(n)). Is the following hierarchy of familiar functions correct?

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A recurrence is any recursively defined function f with domain  that computes numbers. To solve a recurrence f we must find an expression for the general term f(n) that is not recursive. In a simple recurrence, f only appears once on the right side of the general equation for f(n). What method(s) should we use to solve a simple recurrence? Select all that apply.

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