A conditional statement is true if, and only if, its contrapositive is true.
It may or may not be true.
If a conditional statement is true then its contra-positive is also true.
not b not a its contrapositive
A contrapositive means that if a statement is true, than the characteristics also pertains to the other variable as well.
Look at the statement If 9 is an odd number, then 9 is divisible by 2. The first part is true and second part is false so logically the statement is false. The contrapositive is: If 9 is not divisible by 2, then 9 is not an odd number. The first part is true, the second part is false so the statement is true. Now the converse of the contrapositive If 9 is not an odd number, then 9 is not divisible by two. The first part is false and the second part is true so it is false. The original statement is if p then q,the contrapositive is if not q then not p and the converse of that is if not p then not q
example of contrapositive
The statement "All red objects have color" can be expressed as " If an object is red, it has a color. The contrapositive is "If an object does not have color, then it is not red."
Conditional statements are also called "if-then" statements.One example: "If it snows, then they cancel school."The converse of that statement is "If they cancel school, then it snows."The inverse of that statement is "If it does not snow, then they do not cancel school.The contrapositive combines the two: "If they do not cancel school, then it does not snow."In mathematics:Statement: If p, then q.Converse: If q, then p.Inverse: If not p, then not q.Contrapositive: If not q, then not p.If the statement is true, then the contrapositive is also logically true. If the converse is true, then the inverse is also logically true.