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?
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2. Let P(n) be the statement that n2 + n is odd. If P(n) = ⇒ P(n + 1), then P(n) is true:
∀ n > 1
∀ n > 2
None of the above
3. If P(n) : 3n < 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)
5. Given any set of 3 integers, there are 2 integers that have the same remainder when
divided by 3. True or false
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