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

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)

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

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

To find the negation of the statement "p is x-2 is greater and equal to 3," we first need to understand what the statement is saying.

The statement "p is x-2 is greater and equal to 3" can be written in mathematical notation as p ≥ 3. This means that the value of p is greater than or equal to 3.

To find the negation of this statement, we need to change the sign and direction of the inequality. In other words, we want to find the statement that is the opposite of p ≥ 3.

The negation of p ≥ 3 can be written as p < 3. This means that the value of p is strictly less than 3.

So, the answer to your question is: "The negation of p is x-2 is greater and equal to 3 is p is less than 3."