MATH 405 Spring 2014 Midterm 1 Solutions - Solutions...

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Solutions Midterm Exam 1 — Mar. 5, 20141. Determine whether the following statements are true or false.Justify your answer (i.e., prove theclaim, derive a contradiction or give a counter-example).(a) (10 points) IfAB, andBis countable, thenAis countable.
(b) (10 points) IfBis an open cover of (0,1], thenBhas a finite subcover.
Math 405, Fall 2014Solutions to Midterm Exam 1 — Mar. 5, 2014Page 2 of 5(c) (10 points) If [0,1]I1I2. . .In. . .is a nested sequence of closed intervals, thenn=1Inis non-empty.

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