2. LEARNING OBJECTIVES
- determines the relationship between the hypothesis and
the conclusion of an if-then statement
- transforms a statement into an equivalent if-then
statement
- determines the inverse, converse, and contrapositive of
an if-then statement
- illustrates the equivalences of the statement and its
contrapositive, and the converse and inverse of a
statement
3. CONDITIONAL STATEMENTS
Example #1:
State the hypothesis and conclusion of this conditional.
If it is sunny tomorrow, then we will go swimming.
If you drink cold water, then you will be refreshed.
If you think you are great, then you will be great.
4. CONDITIONAL STATEMENTS
Example #2:
Write a conditional statement from the given information.
Hypothesis: You are kind, cheerful, and outgoing.
Conclusion: You will have more friends.
If you are kind, cheerful, and outgoing, then you
will have more friends.
5. CONDITIONAL STATEMENTS
Example #2:
Write a conditional statement from the given information.
Hypothesis: You can admit your mistakes and ask for
apology.
Conclusion: You value relationship than pride.
If you can admit your mistakes and ask for
apology, then you value relationship than pride.
6. CONDITIONAL STATEMENTS
Example #3:
Rewrite the conditional statement in the if-then form.
Help save the environment by recycling bottles, cans,
and papers.
If you recycle bottles, cans, and papers, then
you will help save the environment.
7. CONDITIONAL STATEMENTS
Example #3:
Rewrite the conditional statement in the if-then
form.
You are enough if you think you are enough.
If you think you are enough, then you are
enough.
8. CONDITIONAL STATEMENTS
Example #4:
State in the if-then form. Show that the conditional is false.
All isosceles triangles are right.
Solution:
If-then statement: If a triangle is an isosceles triangle, then it is right.
Hypothesis: ∆𝑋𝑌𝑍 is an isosceles triangle.
Conclusion: ∆𝑋𝑌𝑍 is a right triangle.
∴ The conditional is false. ----- counterexample
Answer TRY
THIS on pages
312 - 313
9. CONVERSE, INVERSE, AND
CONTRAPOSITIVE STATEMENTS
The CONVERSE of a conditional is formed by interchanging the hypothesis and the
conclusion.
Examples:
Statement: If p, then q.
Converse: If q, then p.
Statement: If you are a native Kapampangan, then you are born in Pampanga.
Converse: If you are born in Pampanga, then you are a native Kapampangan.
TRUE
Statement: If you live in Davao, then you live in Mindanao.
Converse: If you live in Mindanao, then you live in Davao.
FALSE
10. CONVERSE, INVERSE, AND
CONTRAPOSITIVE STATEMENTS
When the conditional and its converse are both true, the two
statements can be combined to form a biconditional
statement by using the phrase if and only if.
You are a native Kapampangan if and only if you are born in
Pampanga.
11. CONVERSE, INVERSE, AND
CONTRAPOSITIVE STATEMENTS
The INVERSE of a conditional is formed by negating the hypothesis and the conclusion.
Examples:
Statement: If p, then q.
Inverse: If not p, then not q.
Statement: If you are a native Kapampangan, then you are born in Pampanga.
Inverse: If you are not a native Kapampangan, then you are not born in Pampanga
Statement: If you live in Davao, then you live in Mindanao.
Inverse: If you do not live in Davao, then you do not live in Mindanao.
12. CONVERSE, INVERSE, AND
CONTRAPOSITIVE STATEMENTS
The CONTRAPOSITIVE of a conditional is formed by interchanging the hypothesis and
the conclusion AND negating both.
Examples:
Statement: If p, then q.
Contrapositive: If not q, then not p.
Statement: If you live in Cebu, then you live in Visayas.
Contrapositive: If you do not live in Visayas, then you do not live in Cebu.
Statement: If you have a good heart, then you are a good man.
Contrapositive: If you are not a good man, then you do not have a good heart.
Answer TRY THIS
on pages 314 -
315
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