G8 Math Q2- Week 8- Transforming Contrapositive, Converse and Inverse.pptx
1.
2. Direction: Identify the hypothesis and conclusion
of each conditional statement (if-then) statement
1. If a number is positive integer, then it is a
rational .
Hypothesis: _______________________________
Conclusion: _______________________________
REVIEW
3. Direction: Identify the hypothesis and conclusion
of each conditional statement (if-then) statemen
2. If I study hard, then I will graduate.
Hypothesis: _______________________________
Conclusion: _______________________________
4.
5. OBJECTIVES
determine the if-then, converse, inverse,
contrapositive of a given statement;
transform a statement into if-then, converse,
inverse, and contrapositive statement; and
write a real life statement and transform into
if-then, converse, inverse contrapositive.
8. Consider this statement
“If something is a 20-peso bill, then it has a picture of Manuel L. Quezon
on it.”
Is it the same with the statement “If something has a picture of Manuel L.
Quezon on it, then it is a 20-peso bill.”
9. Switching the hypothesis and conclusion of a conditional statement (if – then form).
Converse
Hypothesis (p): If a shape is a triangle
Conclusion (q) is : then it is a polygon.
Hypothesis (p): If a shape is a Polygon
Conclusion (q) is : then it is a triangle.
Converse
A triangle is a polygon.
Conditional Statement
Statement:
10. CONVERSE
IF-THEN FORM:
If the shape is a triangle, then it is a polygon with three
sides.
CONVERSE:
If the shape is a polygon with three sides, then it is a
triangle.
q p
p q
12. Negating both the hypothesis and conclusion of a conditional statement (if – then form).
Inverse
Hypothesis (p): If a shape is a triangle
Conclusion (q) is : then it is a polygon.
Hypothesis (p): If a shape is NOT a
triangle Conclusion (q) is : then it is
NOT a polygon.
Inverse
Conditional Statement
13. INVERSE
IF-THEN FORM:
If the shape is a triangle, then it is a polygon with three sides.
INVERSE:
If the shape is NOT a triangle, then it is NOT a polygon with three
sides.
p q
～p ～q
14. CONVERSE
IF-THEN FORM:
If a polygon is a quadrilateral, then it has four
sides.
CONVERSE:
If the polygon has four sides, then it is a
quadrilateral.
p
q p
q
15. INVERSE
IF-THEN FORM:
If a polygon is a quadrilateral, then it has four
sides.
INVERSE:
If a polygon is NOT a quadrilateral, then it does NOT have
four sides.
p q
～q
～p
17. Switching the hypothesis and conclusion of
a conditional and negating both.
Contrapositive
Hypothesis (p): If a shape is a triangle
Conclusion (q) is : then it is a polygon.
Hypothesis (p): If a shape is NOT a
Polygon
Conclusion (q) is : then it is NOT a
triangle.
Contrapositive
Conditional Statement
18. CONTRAPOSITIVE
IF-THEN FORM:
If a polygon is a quadrilateral, then it has four
sides.
CONTRAPOSITIVE
If a polygon does not have four sides, then it is NOT a quadrilateral.
p
～ q ～ p
q
19. How do you distinguish the hypothesis
and the conclusion in an if-the
statement?
Can the hypothesis and conclusion be
interchanged?
What is the importance of determining
the hypothesis and the conclusion in the
if-then form?
20.
Use the given statement to complete the
following.
Statement:
If-Then Form: If Juan lives in a congested
area, then he is infected with dengue.
Converse:____________
Inverse: _____________
Contrapositive:________
21.
22. STATEMENT An even number is divisible by two
CONDITIONAL
STATEMENT
CONVERSE
INVERSE
CONTRAPOSITIVE
GROUP 1
A. Fill up the table below.
23. GROUP 2.
From the picture below, write a statement and
transform into if-then, converse, and inverse
statement.
24. CONDITIONAL
STATEMENT
If two angles are congruent, then they have the same
measure.
CONVERSE
INVERSE
CONTRAPOSITIVE
GROUP 3.
B. Fill up the table below.
25.
26.
27. How to transform a statement
into converse?
How to transform a statement
into inverse?
28. We can summarize how to convert the
statement in terms of p and q. study the
table below.
CONDITIONAL
STATEMENT
If p, then q.
CONVERSE If q, then p.
INVERSE If not p, then not q.
CONTRAPOSITIVE If not q, then not p.
32. Content, images, text, etc. used belong to the rightful owner. No
copyright infringement intended.
Editor's Notes
Sino si Manuel L. Quezon
He was the Second President of the Philippines after Emilio Aguinaldo in 1935-1944
he relationship between the hypothesis and the conclusion of an if-then statement is that the hypothesis is the condition that must be satisfied for the conclusion to be true.
Relarionship between the two events. People know that if they see the first event happeniung, then the second will follow. And that is a way of predicting the future
