conditional statements

Conditional Statements

Geometry and Logic

Today’s Warmup

Label a paper for today’s notes9/23/2013 Conditional Statements

Write and finish these sentences.If I don’t do homework, then…If I am late to class, then…If I have a 92% in the class, then…

Conditional Statements

…called conditional statements.

What must exist for something to occur?Premise – Hypothesis (if part of the statement)

Expectation – Conclusion (then part of the statement)

Identify the Parts

If you earn 72%, then you have earned a C.If you go to Disneyland, then you have been to California.If you go to California, then you have been to Disneyland.A triangle is a polygon.Eighth grade algebra students take Pre-AP Geometry.

p → q

Symbolism

Hypothesis (p)Conclusion (q)

Read as “if p then q” or “p implies q.”

Truth Value

either true or false.

Truth Value

If you earn 72%, then you have earned a C.If you have an A, then you are passing.If you have a 58%, then you are failing.If you don’t have DirecTV, then you will sell your hair. If you go to Disneyland, then you have been to California.If you go to California, then you have been to Disneyland.Eighth grade algebra students take Pre-AP Geometry.

Assignment

1., 2., 3. Write conditional statements relating to your life. Identify the hypothesis and conclusion.4. Write an if-then sequential parody using at least 5 conditional statements.

Determine the Truth Value

If Yuli rests for 10 days, her ankle will heal.

Yuli rests for 10 days. She still has a hurt ankle.

true or false

Determine the Truth Value

If Joel rests for 10 days, his ankle will heal.

Joel rests for 3 days. He still has a hurt ankle.

true or false

Determine the Truth Value

If Alexis rests for 10 days, the ankle will heal.

Alexis rests for 10 days and the ankle no longer hurts.

true or false

Determine the Truth Value

If Elijah rests for 10 days, the ankle will heal.

Elijah rests for 7 days. The ankle no longer hurts.

true or false

Evidence of False Statements

If a statement is false, justification is done through a counterexample.

Decide truth value. If false, provide counterexample.

If you earn 72%, then you have earned a C.If you have a passing grade, then you have an A.If you have a 58%, then you are failing.If you go to the Vatican, then you have been to Italy.If you have been to Paris, then you have been to France.If you are tall, then you play basketball.

Negating

Negating means…

Variations of Conditionals

Conditional: p → q Converse: q → p Inverse: ~p → ~ q Contrapositive: ~q → ~p Counterexample: p → ~ q

What’s this got to do with life?

Assignment

1. Find a commercial that uses conditional logic to sell their product. Include a picture of the ad.

a. Write in conditional if-then format. b. Identify the hypothesis and conclusion. c. Write the converse, inverse, and contrapositive form

of the conditional. 2. Write a statement finishing “If two lines are

parallel, then…” regarding angles.a. Identify the hypothesis and conclusion. b. Write the converse, inverse, and contrapositive form

of the conditional.