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Truth Tables and Venn Diagrams

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Truth Tables Truth Tables are a very convenient way to organize the truth values of statements. Disjunction pq Conjunction pq

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Truth Tables pq~p

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Truth Tables pq~p

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Venn diagrams: 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. Example: A = poodle... a dog B = horse... NOT a dog. B DOGS.A.A

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

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To Show Relationships using Venn Diagrams: Blue or Red (includes Purple) …A B AB A B

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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...

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Solution: Three members were on cross country and football teams… 3 The above sentence tells you two draw overlapping circles and put 3 in CC F Twenty-four members of Mu Alpha Theta went to a Mathematics conference. 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. CCFootball 5 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. 1 Continued….

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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 15 Mu Alpha Theta

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