Transcript Hypothesis and conclusion

Section 2-1: Conditional Statements
TPI 32C: Use inductive and deductive reasoning to make conjectures,
draw conclusions, and solve problems
Objectives:
• Recognize conditional statements
• Write converses of conditional statements
Vocabulary
Conditional Statement:
Another name for an If-Then statement
Contains hypothesis and conclusion
Hypothesis: a guess or assumption
Conclusion: inference made from a hypothesis; the result
Converse: switches the hypothesis and conclusion
Conditional Statement
Definition:
A conditional statement is a statement that can be written in
hypothesis
conclusion
if-then form.
“If _____________,
then ______________.”
Conditional Statements have two parts:
1. Hypothesis:
• the given information or condition
• Follows the word “If”
2. Conclusion:
• the result of the given information
• Follows the word “then”
Example:
If your feet smell and your nose runs, then you're built upside
down.
Writing Conditional Statements
Conditional statements can be written in “if-then” form to
emphasize which part is the hypothesis and which is the
conclusion.
Hint: Turn the subject into the hypothesis.
Example 1:
Vertical angles are congruent.
can be written as...
Conditional Statement:
If two angles are vertical, then they are congruent.
Example 2: Seals swim.
can be written as...
Conditional Statement:
If an animal is a seal, then it swims.
Truth Value of Conditional Statements
A conditional statement is false only when the hypothesis is
true, but the conclusion is false.
A counterexample is an example used to show that a
statement is not always true and therefore false.
Statement: If you live in Virginia, then you live in Richmond.
Is there a counterexample?
Yes !!!
Counterexample:
I live in Virginia, BUT I live in Glen Allen.
Therefore () the statement is false.
Exploring a Conditional Statement
Name the hypothesis and conclusion for the following conditional
statements. Can you find a counterexample to make the statement
false?
Conditional statement:
If y – 3 = 5, then y = 8.
Hypothesis (Given): y – 3 = 5
Conclusion (Result): y = 8
Conditional statement:
If it is February, then there are only 28 days.
Hypothesis: It is February
Conclusion: There are only 28 days.
Counterexample: Leap year (2009) has 29 days.
Therefore () the conditional is false.
Write a Conditional Statement
Write a sentence as a conditional (If-then).
A rectangle has four right angles.
(First write two complete sentences; one for the
hypothesis and one for the conclusion)
Hypothesis: A figure is a rectangle. Conditional:
Conclusion: It has four right angles. If a figure is a rectangle, then it
has four right angles.
Write a sentence as a conditional.
A integer that ends with 0 is divisible by 5.
Hypothesis: An integer ends in 0.
Conclusion: It is divisible by 5.
Conditional: If an integer ends in 0, then it is divisible by 5.
Use a Venn Diagram to illustrate a Conditional
Draw a Venn diagram to illustrate the following conditional:
If you live in Chicago, then you live in Illinois.
Residents
Of Illinois
Residents
Of Chicago
Converse of a Conditional Statement
The converse of a conditional is formed by interchanging the
hypothesis and conclusion of the original statement. In other words,
the parts of the sentence change places, but the words “If” and “then”
do not move.
Conditional statement:
"If the space shuttle was launched, then a cloud of smoke was seen."
"If a cloud of smoke was seen, then the space shuttle was launched."
A conditional and its converse can have two different truth values, meaning…
the conditional can be true and its converse can be false.
Ponder this!! Conditional: If a figure is a square, then it has four sides.
Converse: If a figure has four sides, then it is a square.
The converse is false since a rectangle has 4 sides, but is not a square.
Converse of a Conditional Statement
Write the converse of the conditional:
If x = 9, then x + 3 = 12.
The converse of a conditional exchanges the hypothesis and the
conclusion.
Conditional
Converse
Hypothesis
Conclusion
Hypothesis
Conclusion
x=9
x + 3 = 12
x + 3 = 12
x=9
So the converse is: If x + 3 = 12, then x = 9.
Converse of a Conditional Statement
Write the converse of the conditional, and determine
the truth value of each: If a2 = 25, a = 5.
Conditional: If a2 = 25, then a = 5.
The converse exchanges the hypothesis and conclusion.
Converse: If a = 5, then a2 = 25.
The conditional is false.
A counterexample is a = –5: (–5)2 = 25, and –5 =/ 5.
Because 52 = 25, the converse is true.
Symbolic Logic
Symbols can be used to modify or connect statements.
Symbols for Hypothesis and Conclusion:
Hypothesis is represented by “p”.
Conclusion is represented by “q”.
:
if p, then q
or
p implies q
or
pq
Symbolic Logic
Conditional:
Hypothesis and conclusion (p  q)
Converse:
Switch the hypothesis and conclusion (q  p)
pq
If two angles are vertical, then they are congruent.
qp
If two angles are congruent, then they are vertical.
Conditional Statements and Converses
Statement
Example
Symbolic
You read as
Conditional
If an angle is a straight angle,
then its measure is 180º.
pq
If p, then q.
Converse
If the measure of an angle is
180º, then it is a straight
angle
qp
If q then p.
1. Write your own conditional statement on a separate sheet
of paper.
2. Switch your conditional statement with your shoulder
partner.
3. Partners write the hypothesis and conclusion in complete,
separate sentences.
4. Partners switch papers again.
5. Partners write the converse of the conditional statement.
6. Together, partners determine the truth value of their
statements.