Do Now (partner #1) p: you live in San Francisco

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Presentation transcript:

Do Now (partner #1) p: you live in San Francisco q: you live in California Conditional Statement Contrapositive Statement Converse Statement Inverse Statement Is the statement Biconditional?

Do Now (partner #2) p: two angles are complementary. q: the sum of their measure is 90. Conditional Statement Contrapositive Statement Converse Statement Inverse Statement Is the statement Biconditional?

Workbook page 9 H: 3x + 4 = -5 C: x = -3 H: you take a class in television broadcasting C: you will film a sporting event 3) If you do not remember the past, then you are condemned to repeat it.

Workbook page 9 If two angles are adjacent, then they share a common vertex and a common side. True

Workbook page 9 Converse: If -8 > 0, then (-8)2 > 0; true. Inverse: If (-8)2 0, then -8 0; true. Contrapositive: If -8 0, then (-8)2 0; false If you are a junior, then you wait on tables. If you wait on tables, then you are a junior.

2.4 Deductive Reasoning

Law of Detachment Given: If you have a true conditional statement and the hypothesis occurs… pq is true p is given Conclusion: Then, the conclusion will also occur. q is true

Law of Detachment Example 1: Given: If three points are collinear, then the points are all on one line. E, F, and G are collinear. Conclusion: E, F, and G are all on one line.

Law of Detachment Example 2: Given: If I find $20 in the street, then I’ll take you to the movies. On October 10 I found $20 in the street. Conclusion: I will take you to the movies.

Law of Syllogism Given: Two true conditional statements and the conclusion of the first is the hypothesis of the second. pq and qr Conclusion: If the hypothesis of the first occurs, then the conclusion of the second will also occur. pr

Law of Syllogism Example: If it rains today, then we will not have a picnic. If we do not have a picnic, then we will not see our friends. Given: Conclusion: If it rains today, then we will not see our friends.