Math

1. Determining the
Inverse, Converse, and
Contrapositive of an
If-then Statement
Quarter 2 – Module 11

2. The if-then statements, in terms
of p and q, can be converted
into inverse, converse and
contrapositive forms.
The table below summarizes
the converted statements in
terms of p and q.

3. Conditional
Statement
p → q If p, then q
Inverse ~p → ~q
If not p,
then not q
Converse q → p If q, then p
Contrapositive ~q → ~p
If not q,
then not p

4. INVERSE ~p → ~q
To write the inverse of a
conditional statement,
simply negate both the
hypothesis and conclusion.

5. CONVERSE q → p
To write the converse of a
conditional statement, simply
interchange the hypothesis and
the conclusion. That is,
the then part becomes the if
part and the if part becomes
the then part.

6. CONTRAPOSITIVE ~q → ~p
To form the contrapositive of a
conditional statement,
first, get its inverse.
Then, interchange its
hypothesis and conclusion.

7. Conditional
Statement
p → q If p, then q
Inverse ~p → ~q
If not p,
then not q
Converse q → p If q, then p
Contrapositive ~q → ~p
If not q,
then not p

8. Conditional Statement
(If p, then q)
If it is raining,
then the field is wet.
Inverse
(If not p, then not q)
Converse
(If q, then p)
Contrapositive
(If not q, then not p)
If it is not raining,
then the field is not wet.
If the field is not wet,
then it is not raining.
If the field is wet,
then it is raining.

9. Conditional Statement
(If p, then q)
If you do your homework,
then you will pass in Math 8.
Inverse
(If not p, then not q)
Converse
(If q, then p)
Contrapositive
(If not q, then not p)
If you do not do your homework,
then you will not pass in Math 8.
If you do not pass in Math 8, then
you do not do your homework.
If you passed in Math 8,
then you did your homework.

10. QUIZ.
Convert “If-Then” statement into their
Inverse, Converse and Contrapositive.

11. Conditional Statement
(If p, then q)
Inverse
(If not p, then not q)
Converse
(If q, then p)
Contrapositive
(If not q, then not p)

12. Conditional Statement
(If p, then q)
If an object is a triangle,
then it is a polygon.
Inverse
(If not p, then not q)
Converse
(If q, then p)
Contrapositive
(If not q, then not p)
1

13. Conditional Statement
(If p, then q)
If you drink water,
then you obey your thirst.
Inverse
(If not p, then not q)
Converse
(If q, then p)
Contrapositive
(If not q, then not p)
2

14. Conditional Statement
(If p, then q)
If a polygon is a rectangle,
then it has four sides.
Inverse
(If not p, then not q)
Converse
(If q, then p)
Contrapositive
(If not q, then not p)
3

15. Conditional Statement
(If p, then q)
If you are a disciplined person,
then you are God-fearing.
Inverse
(If not p, then not q)
Converse
(If q, then p)
Contrapositive
(If not q, then not p)
4

16. Study Math
for a
Better Path

17. Conditional Statement
(If p, then q)
If an object is a triangle,
then it is a polygon.
Inverse
(If not p, then not q)
Converse
(If q, then p)
Contrapositive
(If not q, then not p)
If an object is not a triangle,
then it is not a polygon.
If an object is not a polygon,
then it is not a triangle.
If an object is a polygon,
then it is a triangle.
1

18. Conditional Statement
(If p, then q)
If you drink water,
then you obey your thirst.
Inverse
(If not p, then not q)
Converse
(If q, then p)
Contrapositive
(If not q, then not p)
If you do not drink water,
then you do not obey your thirst.
If you do not obey your thirst,
then you do not drink water.
If you obey your thirst,
then you drink water.
2

19. Conditional Statement
(If p, then q)
If a polygon is a rectangle,
then it has four sides.
Inverse
(If not p, then not q)
Converse
(If q, then p)
Contrapositive
(If not q, then not p)
If a polygon is not a rectangle,
then it does not have four sides.
If a polygon does not have four sides,
then it is not a rectangle.
If a polygon has four sides,
then it is a rectangle.
3

20. Conditional Statement
(If p, then q)
If you are a disciplined person,
then you are God-fearing.
Inverse
(If not p, then not q)
Converse
(If q, then p)
Contrapositive
(If not q, then not p)
If you are not a disciplined person,
then then you are not God-fearing.
If you are not Godfearing,
then you are not a disciplined person.
If you are Godfearing,
then you are a disciplined person.
4