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Comment : Infimum and Supremum quiz
Comment : This quiz is designed to test your knowledge of order, and specifically
Comment : on infimum and supremum. All sets in this quiz are subsets of the real line R.

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Question 1: Let A and B be bounded non-empty sets. Which of the following statements would be equivalent to saying that inf(A) <= inf(B)?

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	For every b in B and epsilon > 0 there exists an a in A such that a < b + epsilon.
	For every b in B there exists an a in A such that a <= b.
	For every a in A there exists a b in B such that a <= b.
	There exists a in A and b in B such that a < b.
	For every a in A and every b in B, we have a <= b.
	There exists a in A such that a <= b for all b in B.
	There exists b in B such that a < b for all a in A.