Provide counterexamples to the following statements If a and

Provide counterexamples to the following statements. If a and b are integers where a |b and b | a, then a = b. If n^2>0 then n > 0. If n is an even number, then n^2 + 1 is prime. If n is a positive integer, then n^3 >n!.

Solution

Q4.)

a.)Sorry, but I don\'t know what does a|b stands for. If you know that, please do comment and then may be I will able to provide a counterexample.

b.) for n = -2, n^2 =4 >0 but n <0 which contradicts the given statement

c.) for n = 8, n^2 + 1 is 64+1 = 65 which is not prime which contradicts the given statement

d.) for n = 6, n^3 is 216 and n! is 720 which contradicts the given statement

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