HW4_199

# HW4_199 - A 1 Problem 3(2 points If B is a Fnite set and A...

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HOMEWORK 4 DUE: Fri., Oct. 21 NAME: DIRECTIONS: Turn in your homework as SINGLE-SIDED typed or handwritten pages. STAPLE your homework together. Do not use paper clips, folds, etc. STAPLE this page to the front of your homework. Be sure to write your name on your homework. Show all work, clearly and in order . You will lose point 0.5 points for each instruction not followed. Questions Points Score 1 1 2 2 3 2 4 2 5 2 6 1 Total 10 1

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HOMEWORK 4 DUE: Fri., Oct. 21 NAME: Problem 1: (1 point) Show that the composition of bijections is a bijection. Problem 2: (2 points) If A is Fnite and x / A , then A ∪ { x } is Fnite and Card ( A ∪ { x } ) = Card
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Unformatted text preview: ( A ) + 1. Problem 3: (2 points) If B is a Fnite set and A ⊆ B then A is Fnite and Card ( A ) ≤ Card ( B ). Hint: Use induction and problem 2. Problem 4: (2 points) If A is a subset of a countable set B , then A is countable. Hint: Use problem 5 . Problem 5: (2 points) So that if D is a denumerable set and f : D → A is onto, then there is a g : A → D such that g is 1-1. Problem 6: (1 point) (a) (0.5 points) Restate, in your own words, the Axiom of Choice. (b) (0.5 points) Describe, in your own words, Cantor’s Continuum Hypothesis. 2...
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HW4_199 - A 1 Problem 3(2 points If B is a Fnite set and A...

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