Algebra 1 Notes: Lesson 1-7: Logical Reasoning

Objectives Identify hypothesis and conclusion in a conditional statement Write a conditional statement Use counterexamples to prove a statement false Evaluate if a statement is a counterexample

Vocabulary Conditional Statement  If A, Then B

Vocabulary Hypothesis – The A Conclusion – The B

If the popcorn burns, then the heat was too high.

If

If the popcorn burns, Hypothesis

If the popcorn burns, then Hypothesis

If the popcorn burns, then the heat was too high. Hypothesis

If the popcorn burns, then the heat was too high. HypothesisConclusion

Example 1 Identify the hypothesis and conclusion of each statement. If 2x = 4, then x = 2 Hypothesis:

Example 1 Identify the hypothesis and conclusion of each statement. If 2x = 4, then x = 2 Hypothesis: 2x = 4 Conclusion:

Example 1 Identify the hypothesis and conclusion of each statement. If 2x = 4, then x = 2 Hypothesis: 2x = 4 Conclusion: x = 2

Example 1 Identify the hypothesis and conclusion of each statement. I eat light meals Rewrite as if-then:

Example 1 Identify the hypothesis and conclusion of each statement. I eat light meals Rewrite as if-then: If I eat, Then it will be a light meal

Example 1 Identify the hypothesis and conclusion of each statement. I eat light meals Hypothesis:

Example 1 Identify the hypothesis and conclusion of each statement. I eat light meals Hypothesis: I eat Conclusion:

Example 1 Identify the hypothesis and conclusion of each statement. I eat light meals Hypothesis: I eat Conclusion: light meals

Vocabulary Counterexample – A specific case in which a statement is proven false - It only takes ONE to prove a statement false

Example 4 Find a counterexample for the conditional statement. If you are using the Internet, then you own a computer. Assume the hypothesis is true.

Example 4 Find a counterexample for the conditional statement. If you are using the Internet, then you own a computer. Assume the hypothesis is true.

Example 4 Find a counterexample for the conditional statement. If you are using the Internet, then you own a computer. Assume the hypothesis is true. Will the conclusion always be true?

Example 4 Find a counterexample for the conditional statement. If you are using the Internet, then you own a computer. Assume the hypothesis is true. Will the conclusion always be true? No

Example 4 Find a counterexample for the conditional statement. If you are using the Internet, then you own a computer. Assume the hypothesis is true. Will the conclusion always be true? No - You could be using the Internet on a computer at school.

Example 4 Find a counterexample for the conditional statement. If Joe did not eat lunch, then he must be sick.

Example 4 Find a counterexample for the conditional statement. If the traffic light is red, then the car is stopped.

Example 4 Find a counterexample for the conditional statement. If the commutative property is true for multiplication, then it is true for division.

Example 4 Find a counterexample for the conditional statement. If x and y are whole numbers, then x – y ≠ y - x

Example 4 Find a counterexample for the conditional statement. If x ÷ y = 1, then x and y are whole numbers.

Example 4 Find a counterexample for the conditional statement. If you can read 8 pages in 30 minutes, then you can read any book in one day.

Example 4 Find a counterexample for the conditional statement. If x is any number, then x 2 > x

Assignment Pg (all) (all)