Truth Tables and Venn Diagrams

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Presentation transcript:

Truth Tables and Venn Diagrams

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

Truth Tables p q ~p

Truth Tables p q ~p

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 Example:

For all..., every..., if...then... All right angles are congruent. Example1: 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.

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

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...

Solution: 3 Three members were on cross country and football teams… 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….

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