23. Prove that any integers a,9(a?-3)

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Q: Prove (kindly provide reason/s) that for any real numbers m and n, (-m ) + ( - n ) = - ( m + n)

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Q: Find integers ? and ? such that 3220? + 6006? = gcd(3220,6006).

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Q: Prove: For all integers n, if n is odd then n is odd.

A: Given below the detailed solution

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A: Explanation of the answer is as follows

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Q: prove that "The Sum of two odd numbers is even: using direct. Note:- 1 want the ansawer on a paper.

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A: To prove: -m+-n=-m+n Where m and n are real numbers.

Q: Prove 3√3  is irrational

A: See the attachment.

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Q: 3. Show that (5+ 13)e + (5- i3)-" is a real number if is also a real number.

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Q: Prove (n + 6)² – (n + 2)² is always a multiple of 8. (Use direct proof.)

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Q: Show that 2 + V5 is irrational number

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Q: 3. The v77 is between what two integers?

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Q: Use a direct proof to show that the product of two odd numbers is odd.

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Q: 4. Write the following statement symbolically and then prove it: For all real mimbers a and b, if 0…

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Q: Give a proof by contradiction that there does not exist an integer which is both even and odd.…

A: Assume an integer x which is both odd and even.

Q: 2. Show that for any real number x, if x + 2 > 10, then x? – 14 > 5x. Use direct proof.

A: