5. Solve the following problems: 5a. By using proof by cases method, prove that "For all odd integers n, the number n² – 1 is divisible by 8." 5b. By using proof by contradiction technique, prove that "For all integers n, if n² is even then n is even." 5c By using proof by contradiction technique, prove that "V2 is irrational."

Q: How can I prove that if x is a positive irrational number, then 2x-1 is also irrational

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A: Please refer the image below

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Q: irrational

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Q: a. Use the formula S, = (a, + a,) to show that the sum of the first n positive integers is S, = (1 +…

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Q: X7. We know that given any real numbers x1 and x2, if x1X2 0, then x1 0 or x2 = 0. Since there are…

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Q: B. Find a number that provides a counterexample to show that a given statement is false x, x³…

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Q: 6. Prove that x is a rational number if and only if 2x - 1 is a rational number.

A: To Prove: x is a rational number if and only if 2x-1 is a rational number.

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Q: Prove that 2 is irrational. You can use the fact that √2 is irrational.

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A: Given query is to find statement true or false.