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.
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true
if the statement is : if p then q converse: if q then p inverse: if not p then not q contrapositive: if not q then not
Proof!
An Inverse statement is one that negates the hypothesis by nature. This will result into negation of the conclusion of the original statement.
This is not always true.