Conditional Statements power point.ppt...

easy way to discuss the conditional statement

1. Consider these advertisements:Consider these advertisements:
1. If you want a straight and shiny hair, then
use cream silk.
2. If you want a slim body, then drink fit and
right.

2. Questioning:Questioning:
1. What are the words used in the two
advertisements in the hope that consumers will
believe their advertising claims?
2. In mathematics, what do you call “if-then”
statement?
3. What do you call the “if” part? How about
the “then” part?

3. Consider these advertisements:Consider these advertisements:
1. If you want a straight and shiny hair, then
use cream silk.
2. If you want a slim body, then drink fit and
right.

These advertisements use “if-then” statement in the
hope that consumers will believe their advertising claim.
In mathematics, an if-then statement is called a
conditional statement. The if part is the hypothesis
and the then part is the conclusion.

4. CONDITIONAL STATEMENTSCONDITIONAL STATEMENTS
and its related statements
(Converse, Inverse and Contrapositive statements)

5. What you’ll learn:What you’ll learn:
Identify the hypothesis and conclusion of
If-Then and other related statements.
Formulate the converse, inverse and
contrapositive of a conditional statement
Determine the truth value of the given
conditional statement and its related
statement

6. Conditional StatementsConditional Statements
Conditional - Conditionals are formed by joining
two statements with the words if and then: If p,
then q.
The if-statement is the hypothesis and the then-
statement is the conclusion.
Conditional statements are either true conditionals
or false conditionals. A conditional is a false
conditional when the hypothesis is true and the
conclusion is false. A conditional can be shown
to be false by using a counterexample.

8. Identify Hypothesis and Conclusion
A. Identify the hypothesis and conclusion of the following
statement.
If a polygon has 6 sides, then it is a hexagon.

9. Identify Hypothesis and Conclusion
A. Identify the hypothesis and conclusion of the following
statement.
Answer:Hypothesis: a polygon has 6 sides
Conclusion: it is a hexagon
If a polygon has 6 sides, then it is a hexagon.
If a polygon has 6 sides, then it is a hexagon.
hypothesis conclusion

10. Identify Hypothesis and Conclusion
B. Identify the hypothesis and conclusion of the following
statement.
Tamika will advance to the next level of play if she
completes the maze in her computer game.

11. Identify Hypothesis and Conclusion
B. Identify the hypothesis and conclusion of the following
statement.
Tamika will advance to the next level of play if she
completes the maze in her computer game.
Answer:Hypothesis: Tamika completes the maze in her
computer game
Conclusion: she will advance to the next level of
play

12. Write a Conditional in If-Then Form
B. Identify the hypothesis and conclusion of the following
statement. Then write the statement
in the if-then form.
A five-sided polygon is a pentagon.

13. Write a Conditional in If-Then Form
B. Identify the hypothesis and conclusion of the following
statement. Then write the statement
in the if-then form.
A five-sided polygon is a pentagon.
Answer:Hypothesis: a polygon has five sides
Conclusion: it is a pentagon
If a polygon has five sides, then it is
a pentagon.

14. A. Determine the truth value of the following statement for
each set of conditions. If Yukon rests for 10 days, his ankle
will heal.
Truth Values of Conditionals
Yukon rests for 10 days, and he still has a hurt ankle.

15. A. Determine the truth value of the following statement for
each set of conditions. If Yukon rests for 10 days, his ankle
will heal.
Answer:Since the result is not what was expected, the
conditional statement is false.
Truth Values of Conditionals
The hypothesis is true, but the conclusion is false.
Yukon rests for 10 days, and he still has a hurt ankle.

16. B. Determine the truth value of the following statement for
each set of conditions. If Yukon rests for 10 days, his ankle
will heal.
Truth Values of Conditionals
Yukon rests for 3 days, and he still has a hurt ankle.

17. B. Determine the truth value of the following statement for
each set of conditions. If Yukon rests for 10 days, his ankle
will heal.
Answer:In this case, we cannot say that the statement is
false. Thus, the statement is true.
Truth Values of Conditionals
The hypothesis is false, and the conclusion is false. The
statement does not say what happens if Yukon only rests for
3 days. His ankle could possibly still heal.
Yukon rests for 3 days, and he still has a hurt ankle.

18. C. Determine the truth value of the following statement for
each set of conditions. If Yukon rests for 10 days, his ankle
will heal.
Truth Values of Conditionals
Yukon rests for 10 days, and he does not have a hurt
ankle anymore.

19. C. Determine the truth value of the following statement for
each set of conditions. If Yukon rests for 10 days, his ankle
will heal.
Answer:Since what was stated is true, the conditional
statement is true.
Truth Values of Conditionals
The hypothesis is true since Yukon rested for 10 days, and
the conclusion is true because he does not have a hurt ankle.
Yukon rests for 10 days, and he does not have a hurt
ankle anymore.

20. D. Determine the truth value of the following statement for
each set of conditions. If Yukon rests for 10 days, his ankle
will heal.
Truth Values of Conditionals
Yukon rests for 7 days, and he does not have a hurt ankle
anymore.

21. D. Determine the truth value of the following statement for
each set of conditions. If Yukon rests for 10 days, his ankle
will heal.
Answer:In this case, we cannot say that the statement is
false. Thus, the statement is true.
Truth Values of Conditionals
The hypothesis is false, and the conclusion is true. The
statement does not say what happens if Yukon only rests for
7 days.
Yukon rests for 7 days, and he does not have a hurt ankle
anymore.

22. Conditionals, Converses, etc.Conditionals, Converses, etc.
Conditional - If p, then q.
Converse - If q, then p.
Inverse – If not p, then not q.
Contrapositive – If not q, then not p.
Rules of Logic:
The truth value of a converse may or may not be the
same as that of its conditional.
The truth value of a conditional and its contrapositive are
always the same. Likewise for a converse and an inverse.

24. Write the converse, inverse, and contrapositive of the
statement All squares are rectangles. Determine whether
each statement is true or false. If a statement is false, give a
counterexample.
Related Conditionals

25. Write the converse, inverse, and contrapositive of the
statement All squares are rectangles. Determine whether
each statement is true or false. If a statement is false, give a
counterexample.
Related Conditionals
Conditional:If a shape is a square, then it is a
rectangle.
The conditional statement is true.
First, write the conditional in if-then form.
Write the converse by switching the hypothesis and
conclusion of the conditional.
Converse: If a shape is a rectangle, then it is a
square. The converse is false. A rectangle with and w =
4 is not a square.

26. Inverse: If a shape is not a square, then it is not a
rectangle. The inverse is false. A 4-sided polygon with side
lengths 2, 2, 4, and 4 is
not a square.
The contrapositive is formed by negating the hypothesis and
conclusion of the converse.
Contrapositive: If a shape is not a rectangle,
then it is not a square.
The contrapositive statement is true.
Related Conditionals

27. Write the converse, inverse, and contrapositive of the
statement A triangle with no sides congruent is scalene .
Determine whether each statement is true or false. If a
statement is false, give a counterexample.
Related Conditionals

28. Write the converse, inverse, and contrapositive of the
statement A triangle with no sides congruent is scalene .
Determine whether each statement is true or false. If a
statement is false, give a counterexample.
Related Conditionals
Conditional:If a triangle has no sides congruent, then it
is
scalene.
The conditional statement is true.
First, write the conditional in if-then form.
Write the converse by switching the hypothesis and
conclusion of the conditional.
Converse: If a triangle is scalene, then it has no sides
congruent.
The converse statement is true.

29. Inverse: If a triangle has congruent sides, then it is not
scalene.
The conditional statement is true.
The contrapositive is formed by negating the hypothesis and
conclusion of the converse.
Contrapositive: If a triangle is not scalene,
then it has
congruent sides.
The contrapositive statement is true.
Related Conditionals