Actual Midterm 1 Solutions - Solutions Midterm Exam 1 Feb 23 2015 1 Let be an equivalence relation on N(a(10 points Give the formal denition the

Actual Midterm 1 Solutions - Solutions Midterm Exam 1 Feb...

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Solutions Midterm Exam 1 — Feb. 23, 2015 1. Letbe an equivalence relation onN.(a) (10 points) Give the formal definition the equivalence class [n] of an elementnNwith respecttoand the formal definition of the quotient spaceN/as a subset of the power-setP(N). (b) (15 points) Show that if each equivalence class ofcontains only finitely many elements, thenthe quotient spaceX=N/is countable.

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