Use one of the methods: direct proof, contraposition, contradiction, or a counterexample to prove or disprove each statement. Every method must be used once and only once. (1). For all integers n > 2,n² – n – 1 is prime. (2). The product of three consecutive integers is always divisible by 3. (3). V x, y E Z,if x³ + y³ is even, then is x + y even.
Use one of the methods: direct proof, contraposition, contradiction, or a counterexample to prove or disprove each statement. Every method must be used once and only once. (1). For all integers n > 2,n² – n – 1 is prime. (2). The product of three consecutive integers is always divisible by 3. (3). V x, y E Z,if x³ + y³ is even, then is x + y even.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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please someone do this asap please please please. show all the work step by step and do each part PLEASE.
Transcribed Image Text:Use one of the methods: direct proof, contraposition, contradiction, or a counterexample to prove or disprove each
statement. Every method must be used once and only once.
(1). For all integers n > 2,n² - n – 1 is prime.
(2). The product of three consecutive integers is always divisible by 3.
(3). Vx, y E Z,if x³ + y³ is even, then is x + y even.
(4). log,21 is an irrational number.
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