1- it is not raining and it is not snowing.

Negation:
It is raining or it is snowing.

[Notice that the negation of an "and" statement is the negations of the parts
with an "or" between them, and vice versa, a rule which is known as 
DeMorgan's law.
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2- x is greater than y .

Negation:
x is not greater than y.

The negation can also be worded as 

x is less than or equal to y.

[Be sure not to leave out "or equal to".]

Edwin