Contrapositive, Converse and Inverse

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 ~(x 1 or x 0)    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 x 1 or x 0.   If x2 > x for some integer x, then x is not equal to 1 or 0. Converse x Z, if ~(x 1 or x 0), 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 