What is the inverse of the sentence "If i win, then I'm happy." ?
There are several different possibilities:
There are several different concepts in English that involve the inverse of a sentence. Each concept yields a different result and therefore a different meaning.
Reversing the clause
Essentially all you need to do is reverse the two clauses. For example what I did here was take the first clause "If I win . . ." and switch it with the second clause ". . . then I'm happy.", which gives us this statement:
Then I'm happy, if I win."
Since the first word is an adverb and in this sentence it isn't modifying (describing) a verb we can just remove it from the sentence. If we remove "then" from the sentence we get:
"I'm happy, if I win."
The inverse could also pertain to the affirmation or negation of the statement. In this case all we would do change the statement which is in the affirmative (it expresses validity or truth, it is "positive") to change it to a negative statement all we need to do is add "not" to both clauses to get:
"If I do not win, then I will not be happy."
To enhance the sentence's flow (or at least what I see as flow [it could be just a colloquial preference]) we can create contractions by converting ". . . do not . . ." to "don't" and ". . . will not. . ." to "won't" this leaves us with:
"If I don't win, then I won't be happy."
As my friend Steek mentions below that too is also a possibility of inverting the sentence. So to conclude, English is funny in that there are many methods of playing with a sentence to invert either it's structure or its meaning.
I hope this helps!