Consider the proposition,
Vandana's smartphone has at least 32 GB of memory.
Three valid negations are,
It is not the case that Vandana's smartphone has atleast 32GB of memory.
Vandana's smartphone does not have atleast 32GB of memory.
Vandana's smartphone has less than 32GB of memory.
I am wondering if I put it like this,
Vandana's smartphone has 2GB of memory.
Is that still a valid negation to the above proposition ? I am wondering,any value less than 32GB could possibly negate that poroposition ? (I arbitrarily used the value '2')
(This example is taken from Section 1.1 of Discrete Mathematics and Apllications by Kenneth H Rosen)
The negation of $x\geq 32$ is not going to be $x=2$. You will want to make a claim that will be true for any viable value of $x$ that makes $x\geq 32$ false, not just a particular example.