Use indirect reasoning to show that for a natural number n, if n^2 is odd then n is also odd. ( this problem shows the value of algebra in a proof) note that the given statement is in the form P~>, Or "if p, then g" Choose the statement that correspond to p. [ln is odd [] n^2is odd [lIf n^2 is odd then n is odd

Write the following statement as a mathematical statement. Use variable names to denote arbitrary numbers in the domain. Your statements and should be expressed using algebra. "There is no largest integer."

True or False. Explain why? Justify your answer mathematically. Use examples, counterexamples, definitions or previously proven properties to support your answer (if needed).

Prove the 8 divisibility test for ANY number. This should be a mathematical proof, not a word or paragraph proof.    DO NOT write a proof that is for just a four-digit number or a five-digit number.  If you do that then you are not proving it for ANY number.  You must prove it for ANY number by proving that 8 | (10n-1an-1 + 10n-2an-2 + 10n-3an-3 + … + 100a2 + 10a1 + a0).   without modular

not use ai please

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