"If ~A then ~B" where ~A means the opposite of A. For example if A is "it rains all week" and B is "it rains on Tuesday" then if A then B is "if it rains all week, it rains on Tuesday" while if ~A then ~B is "if it doesn't rain all week, it doesn't rain on Tuesday" which doesn't necessarily have the same truth value as the first.
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The negation of B is not between A and C is = [(A < B < C) OR (C < B < A)] If A, B and C are numbers, then the above can be simplified to (B - A)*(C - B) > 0
No, the inverse is not the negation of the converse. Actually, that is contrapositive you are referring to. The inverse is the negation of the conditional statement. For instance:P → Q~P → ~Q where ~ is the negation symbol of the sentence symbols.
Definition by negation is a solution to a right angle statement.
Negation is a logical connective. In philosophy, it means that it takes truth to a falsehood, and falsehood to a truth.
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