(8) "Axioms" or "postulates" are statements that are assumed, without further justification, whereas "theorems" or "proposi- tions" are proved using the axioms. pressed as a quotient of two whole numbers. ematical statements to make sure they were correct. (9) We call V2 an "irrational number" because it cannot be ex- (10) The ancient Greeks were the first to insist on proofs for math-

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A: Given To prove that a-b is irrational number if a and b are prime number.

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Q: 13. Prove 7 + √2 irrational

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Q: -, 1+2+2 '+.+ 2 -1 for all natural numbers n.

A: We will use the principle of mathematical induction to prove the result.

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A: The explanation of the solution as follows:

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A: Given: To prove that if n is an integer and 3n+2 is even then n is even.

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Q: irrational

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Q: Prove 3√3  is irrational

A: See the attachment.

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Q: 1. Prove that 5 is irrational. 2. Prove that 3 + 25 is irrational.

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A: We have to find the terms

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Q: The ancient Greek were the first to insist on proofs for Mathematician statement to make sure they…

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Q: 4. Given that √2 is an irrational number. Show that 5+ 3√2 is an irrational number.

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A: