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1. Suppose 6 pairs of similar-looking boots are thrown in a pile. How many boots must you pick in order to be sure of getting a matched pair?

7

6

3

2

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2. Let P(n) be the statement that n^{2} + n is odd. If P(n) = ⇒ P(n + 1), then P(n) is true:

∀ n

∀ n > 1

∀ n > 2

None of the above

3. If P(n) : 3^{n} < n!, n ∈ N, then P(n) is true for:

n ≥ 7

n ≤ 7

n = 7

n > 7

4. How many integers from 100 to 999 must be picked in order to be sure that atleast 2 of them have a digit in common? (For example, 256 and 530 have the digit 5 in common)

10

5. Given any set of 3 integers, there are 2 integers that have the same remainder when divided by 3. True or false

True

False

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