Conditional statement is a statement with a hypotesis and a conclusion:
If , then
or mathematically
.
Converse statement of is statement
.
If you negate (that means stick a "not" in front of) both the hypothesis and conclusion, you get the inverse:
.
Finally, if you negate everything and flip p and q (taking the inverse of the converse) then you get the contrapositive:
.
Example:
1. Statement: If it is raining, then I'm at home. (true)
2. Converse: If I'm at home, then it is raining. (not necessarily true)
3. Inverse: If it is not raining, then I'm not at home. (not necessarily true)
4. Contrapositive: If I'm not at home, then it is not raining. (true)
