4. Prove the given statements by the indicated method.(1). By Direct Proof: “Vm, n € Z+ − {1}, m² | n² ↔ m [n.” ·(2). By Contraposition: “V n, p, q € Z* U {0}, n+2p+3q ≥ 5 → (n ≥ 3) v (p ≥ 2) V (q ≥ 1)."(3). By Contradiction: "V x, y, z € R, x + y, x+z, and y + z € Q → x, y, and z € Q.¹

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Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section: Chapter Questions

Problem 63RE

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Prove the given statements by the indicated method. (1). By Direct Proof: "Vm, n € Z+ - {1}, m² | n² → m n."