Question

If p is x-2 is greater and equal to 3, what is the negation of p?

Answer 1

x-2 ≥ 3 (+2 to each side)
x ≥ 5

since p = x-2, p will always be positive
(lowest value of x is 5, which would make p = 5-2 = 3, i.e. positive)

Answer 2

since the opposite of "greater than or equal" is "less than",

~p = ~(x-2 >= 3) = x-2 < 3