Answers:

1.If it's snowing, then the weather must be cold outside.

weather w, if it's snowing, then w is cold.	Formal logical format
weather w, if ~(w is cold), then ~(it's snowing).   If it isn't cold outside, then it's not snowing.	Contrapositive
weather w, if w is cold, then it's snowing.   If it's cold outside, then it must be snowing.	Converse
weather w, if ~(it's snowing), then ~(w is cold).   If it isn't snowing, then it must not be cold outside.	Inverse

2.  If an integer x does not equal 1 or 0, then x² is greater than x.

x Z, if x 1 or x 0, then x2 > x.	Formal logical format
x Z, if ~(x2 > x), then ~(x1 or x0)    or... x Z, if x2 < x, then x = 1 or x = 0.   If x2 < x for some integer x, then x = 1 or x = 0	Contrapositive
x Z, if x2 > x, then x1 or x0.   If x2 > x for some integer x, then x is not equal to 1 or 0.	Converse
x Z, if ~(x1 or x0), then ~(x2 > x).   If an integer x equals 1 or 0, then x2 is less than or equal to x.	Inverse

3.  If a student gets caught cheating, he/she will receive a grade of "F".

students s, if s is caught cheating then s will receive a grade of "F".	Formal logical format
students s, if ~(s will receive a grade of "F") then ~(s is caught cheating).        or students s, if s does not receive a grade of "F" then s was not caught cheating.   If a student did not receive a grade of "F", then he/she was not caught cheating.	Contrapositive
students s, if s receives a grade of "F" then s was caught cheating.   If a student receives a grade of "F", then he/she was caught cheating.	Converse
students s, if ~(s is caught cheating) then ~(s will receive a grade of "F").       or students s, if s is not caught cheating then s will not receive a grade of "F".   If a student is not caught cheating, then he/she will not receive a grade of "F".	Inverse