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Counterexample: n= 1
n²+1 = 2

Solving the expression, it is found a counterexample that when [tex]n = 1[/tex], [tex]n^2 + 1 = 2[/tex] is even.

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  • The expression given is:

[tex]E(n) = n^2 + 1[/tex]

  • We want to test for every integer n, that E(n) is odd.

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For n = 0:

[tex]E(0) = 0^2 + 1 = 0 + 1 = 1[/tex]

Odd number.

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For n = 1:

[tex]E(1) = 1^2 + 1 = 1 + 1 = 2[/tex]

Even, thus, this is the counterexample.

A similar problem is given at https://brainly.com/question/17784562

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