4. Write an analysis of proof for each proposition below by using construction method. a) If a, b, and c are integers for which a|b, and blc, then alc. b) Ifn is an integer and n is an odd integer, then n² + 3 is divisible by 2. c) If p and q are rational and q + 0, then 2 is rational. d) If the function f(x) = Vx + 1 is continuous in the interval [0,3), then there exists a value c that satisfy the Mean Value Theorem for integral. e) Prove that if m < n are consecutive integers and m is even, then 4 divides m? + n2 – 1.

4. Write an analysis of proof for each proposition below by using construction method. a) If a, b, and c are integers for which a|b, and blc, then alc. b) Ifn is an integer and n is an odd integer, then n² + 3 is divisible by 2. c) If p and q are rational and q + 0, then 2 is rational. d) If the function f(x) = Vx + 1 is continuous in the interval [0,3), then there exists a value c that satisfy the Mean Value Theorem for integral. e) Prove that if m < n are consecutive integers and m is even, then 4 divides m? + n2 – 1.

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter10: Inequalities

Section10.2: Solving Inequalities

Problem 62WE

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