Chapter 2Reasoning & Proof

2 – 1 Conditional Statements

Objectives:

To recognize conditional statements

To write converses of conditional statements

“If you are not completely satisfied, then your money will be refunded.”

an if-then statementConditional:

Hypothesis:

Conclusion:the part of the conditional that follows “if”

the part of the conditional that follows “then”

Example 1 Identifying the Hypothesis & Conclusion

Identify the hypothesis and the conclusion of each conditional statement.

A. If today is the first day of fall, then the month is September.

B. If y – 3 = 5, then y = 8.

Example 2 Writing a ConditionalWrite each sentence as a conditional.

A. A rectangle has four right angles.

B. A tiger is an animal

C. An integer that ends with 0 is divisible by 5

D. A square has four congruent sides

Truth Value:

TRUE: every time the hypothesis is true, the conclusion is also true.

either TRUE or FALSE

FALSE: find ONE counterexample for which the hypothesis is true and the

conclusion is false.

Example 3 Finding a Counterexample

Show that this conditional is false by finding a counterexample:

A) If it is February, then there are only 28 days in the month.

Show that this conditional is false by finding a counterexample.

B) If the name of a state contains the word New, then the state borders an ocean.

Example 4 Using a Venn Diagram

A) Draw a Venn diagram to illustrate this conditional.

If you live in Little Falls, then you live in New Jersey.

B) Draw a Venn diagram to illustrate this conditional

If something is a whole number, then it is an integer.

Homework :Page 71 – 72; 2 – 22 Even

2 – 1 Continued Objective:

To write converses of conditional statements

Converse:Switches the hypothesis and conclusion of a conditional

Conditional: If an angle has measure 40, then it is acute.

Converse: If an angle is acute, then it has measure 40.

Example 5 Writing the Converse of a Conditional

Write the converse of the following conditional.

A) If two lines intersect to form right angles, then they are perpendicular.

Write the converse of the following conditional.

A) If two lines intersect to form right angles, then they are perpendicular.

Converse: If two lines are perpendicular, then they intersect to form right angles.

B) Write the converse of the following conditional.

If two lines are not parallel and do not intersect, then they are skew.

Converse: If two lines are skew, then they are not parallel and do not intersect.

B) Write the converse of the following conditional.

If two lines are not parallel and do not intersect, then they are skew.

Example 6 Finding the Truth Value of a ConverseConsider this true conditional statement. Write the converse and determine its truth value.

A) If a figure is a square, then it has four sides.

Converse: If a figure has four sides, then it is a square.Truth Value of Converse: FALSE

Write the converse of each conditional statement. Determine the truth value of the conditional and its converse.

B) If two lines do not intersect, then they are parallel.

C) If x = 2, then =2.

Example 7 Real-World Connection

“Why you might just as well say that ‘I see what I eat’ is the same thing as ‘I eat what I see’!” – Mad Hatter

A) Explain why the Mad Hatter is wrong.

“Why you might just as well say that ‘I see what I eat’ is the same thing as ‘I eat what I see’!” – Mad

Hatter

B) Explain why the Dormouse is wrong.

“…’I breathe when I sleep’ is the same thing as ‘I sleep when I breathe’!”

– Dormouse

Ticket OutUse “If a circle’s radius is 2m, then its diameter is 4m” to answer # 1 – 3.

1) Identify the hypothesis & conclusion

2) Write the converse

3) Determine the truth value of the conditional and its converse (include counterexamples if necessary)

4) True or False? If lines do not intersect, then they are parallel.

5) True or False? All numbers containing the digit 0 are divisible by 10.

Homework

Textbook Page 37; # 23 – 35 All