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1. All prime numbers are odd

Universal Statement:
For all x in mathbb{N} such that for any a,b in mathbb{N}
x = ab where a or b must be equal to 1 and for any k in mathbb{N}, x = 2k + 1

Counterexample will comprise of:
A counterexample will be an x in mathbb{N} such that there exists a k in mathbb{N}
such that x = 2k

Counterexample:
2


6. For all real numbers x, we have x^2-2x+2 > 1

Universal Statement:
For all x in mathbb{R}, we have x^2-2x+2 > 1

Counterexample will comprise of:
A counterexample will be an x such that x^2-2x+2 < 1

Counterexample:
1


14. For all functions f : mathbb{R} rightarrow mathbb{R}, if f is not increasing,
then it must be decreasing.

Universal Statement:
For all functions f : mathbb{R} rightarrow mathbb{R} for all x_1, x_2 if
x_1 < x_2 and f(x_1) ngeq f(x_2) then f(x_1) leq f(x_2)

Counterexample will comprise of:
A counterexample will be a function f such that for all x_1, x_2 if x_1 < x_2 and
f(x_1) ngeq f(x_2) then f(x_1) nleq f(x_2)

Counterexample:
None, the statement is true

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