Lesson 2-2 Logic Lesson 2-2: Logic.

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Lesson 2-2 Logic Lesson 2-2: Logic

Venn diagrams: . .A show relationships between different sets of data. can represent conditional statements. is usually drawn as a circle. Every point IN the circle belongs to that set. Every point OUT of the circle does not. A =poodle ... a dog B= horse ... NOT a dog . B DOGS .A ...B   dog Example: Lesson 2-2: Logic

For all..., every..., if...then... Example1: All right angles are congruent. Congruent Angles Example 2: Every rose is a flower. Right Angles Flower lines that do not intersect Rose parallel lines Example 3: If two lines are parallel, then they do not intersect. Lesson 2-2: Logic

To Show Relationships using Venn Diagrams: B A  B Blue or Brown (includes Purple) … AB Lesson 2-2: Logic

Example: Twenty-four members of Mu Alpha Theta went to a Mathematics conference. One-third of the members ran cross country. One sixth of the members were on the football team . Three members were on cross country and football teams. The rest of the members were in the band. How many were in the band? Hint: Draw a Venn Diagram and take one sentence at a time... Lesson 2-2: Logic

Solution: Twenty-four members of Mu Alpha Theta went to a Mathematics conference. Three members were on cross country and football teams… CC Football 3 1 5 The above sentence tells you two draw overlapping circles and put 3 in CCF One-third of the members ran cross country. 24 / 3 = 8; 8 members run cross country. So put 5 in cross country as there are already 3 in cross country. One sixth of the members were on the football team . 24/6 = 4; 4 members play football. So put 1 in football as there are already 3 in football. Continued…. Lesson 2-2: Logic

Example: Continued…… The rest of the members were in the band. How many were in the band? Out of 24 members in Mu Alpha Theta, 9 play football or run cross country. Therefore, 15 are in the band. CC Football Band 3 5 1 15 Mu Alpha Theta Lesson 2-2: Logic

Law of Detachment Given: a true conditional statement and the hypothesis occurs pq is true p is given Conclusion: the conclusion will also occur q is true Lesson 2-2: Logic

Law of Detachment - Example 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. 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. Lesson 2-2: Logic

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 Lesson 2-2: Logic

Law of Syllogism - Example Given: 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. Conclusion: If it rains today, then we will not see our friends. Lesson 2-2: Logic