Write a formal proof for the following biconditional statement. For all integers n, n^3 is even if and only if n is even. [Hint: For one of the two directions of this proof, you might want to consider a proof using the contrapositive.] [Reminder: You may use the parity property, which states that each integer is either even or odd, but not both.]

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A: The answer is given below:-

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A:

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A:

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A: Answer is in next step.

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Q: We are interested to see divisibility checking of only prime numbers in base 10. For a prime P, you…

A: The complete code is given below with output .

Q: How many methods of proof are there? Use a direct proof to show that the sum of two even integers is…

A: How many methods of proof are there? Use a direct proof to show that the sum of two even integers is…

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A: Solution: Introduction:

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A: Answer is given below   a) P(1): 1^3 = (1(1+1)/2)^2 b) 1^3 = 1 (1(1+1)/2)^2 = (2/2)^2 = 1^2 = 1…

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A: This can be checked using the bitwise and operator. Basic idea is to perform bitwise and between the…