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 statementContains 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 if-then form. “If _____________, then ______________.”

Example:

If your feet smell and your nose runs, then you're built upside down.

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”

hypothesis conclusion

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...

If two angles are vertical, then they are congruent.

Conditional Statement:

Example 2: Seals swim.

can be written as...

Conditional Statement:If an animal is a seal, then it swims.

Writing 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.

If you live in Virginia, then you live in Richmond.Statement:

Counterexample:

I live in Virginia, BUT I live in Glen Allen.

Is there a counterexample?

Therefore () the statement is false.

Yes !!!

Truth Value of Conditional Statements

Exploring a Conditional Statement

Conditional statement:If it is February, then there are only 28 days.

Conditional statement:If y – 3 = 5, then y = 8.

Name the hypothesis and conclusion for the following conditional statements. Can you find a counterexample to make the statement false?

Hypothesis (Given): y – 3 = 5Conclusion (Result): y = 8

Hypothesis: It is FebruaryConclusion: There are only 28 days.

Counterexample: Leap year (2009) has 29 days.

Therefore () the conditional is false.

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.Conclusion: 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.

Write a Conditional Statement

Conditional: If a figure is a rectangle, then it has four right angles.

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

ResidentsOf Chicago

Converse of a Conditional Statement

Conditional statement: "If the space shuttle was launched, then a cloud of smoke was seen."

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.

"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.

Write the converse of the conditional: If x = 9, then x + 3 = 12.

The converse of a conditional exchanges the hypothesis and the conclusion.

So the converse is: If x + 3 = 12, then x = 9.

Conditional

Hypothesis Conclusion Hypothesis Conclusion

x = 9 x + 3 = 12 x + 3 = 12 x = 9

Converse

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.

Because 52 = 25, the converse is true.

The conditional is false. A counterexample is a = –5: (–5)2 = 25, and –5 5.=/

Converse of a Conditional Statement

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 qor

Symbolic Logic

p q:

Converse:

Switch the hypothesis and conclusion (q p)

pq If two angles are vertical, then they are congruent.

qp If two angles are congruent, then they are vertical.

Symbolic Logic

Conditional: Hypothesis and conclusion (p q)

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.