Determining the Inverse, Converse, and Contrapositive of an If-then Statement [Autosaved].pptx

Math 8 Q2

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 S tatement (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 , t hen it is not raining. If the field is wet , t hen it is raining.

9. Conditional S tatement (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. QU IZ. Convert “If-Then” statement into their Inverse, Converse and Contrapositive.

11. Conditional S tatement (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 S tatement (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 S tatement (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 S tatement (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 S tatement (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 S tatement (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 S tatement (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 S tatement (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 S tatement (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