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Section 2.3

Thursday, September 18, 2008

1. Warmup: Worksheet 2.1 2. Teach 2.3 a. Worksheet 2.3A b. Worksheet 2.3B 3. Quiz Review 2.1-2.3 4. Homework: Review Worksheet 2.1-2.3 a. Quiz Tomorrow 2.1-2.3

Math 217 Section 2.3A

Name _________________________

A Venn Diagram can be used to represent a conditional statement. If it is raining, then it is cloudy. If you study, then you get a good grade.

Law of Detachment

If p q is a true statement, and p is true, then q is true. Venn Diagram: Symbolic Logic:

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Examples: 1. If today is Halloween, then you wear a costume. Today is Halloween. What can you conclude? Venn Diagram: Conclusion:

2. If you want a steak that is grilled to perfection, then go to Morton's. Brandon went to Morton's.

What can you conclude? Venn Diagram: Conclusion:

Law of Syllogism

If p q and q r are true conditionals, then p r is also true. Venn Diagram: Symbolic Logic:

p q p

q r r

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Examples: 1. If a metal is liquid at room temperature, then it is mercury. If a metal is mercury, then its chemical symbol is Hg. What can you conclude?

Venn Diagram: Conclusion:

2. If two angles are a linear pair, then they are supplementary. If two angles are supplementary, then the sum of their measures is 180. What can you conclude? Venn Diagram: Conclusion:

3. If a triangle is equilateral, then it is equiangular. If a triangle is equiangular, then each angle measures 60 . What can you conclude?

Venn Diagram: Conclusion:

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Math 217 Section 2.3B

Name ________________________

Venn Diagrams a. Write a Conditional statement (or two) to represent the situation. b. Make a Venn Diagram for each of the statements below. c. What can you logically conclude in each case? d. Write D if you used the Law of Detachment, S if you used the Law of Syllogism, and N if there is No Valid conclusion.

1. All students enjoy math. Jason is a student.

2. Athletes are fit. Andrea is fit.

3. If two angles form a linear pair, then they are adjacent.

1 and

2 are a linear pair.

4. If it is October, then it is Fall. If it is Fall, then the leaves change color.

5. SHS students are Saxons. Saxons are a Class Act.

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6. 1 and

2 are complementary. Complementary angles sum to 90°.

7. Well-known athletes appear on Wheaties. Michael Jordan appeared on Wheaties.

8. The sun is a star. Stars are in constant motion.

9. Vertical angles are congruent.

A and

B are vertical angles.

10. Perpendicular lines intersect. Line x and Line y are perpendicular.

11. All integers are real numbers. 7 is an integer.

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12. All integers are real numbers.

is a real number.

13. The sun is a star. A giant nova is a star.

14. The sun is a star. Stars are very hot and bright.

Math 217 Quiz Review 2.1-2.3A

Name: _______________________

1. Underline the hypothesis and circle the conclusion of the conditional statement: A) If an angle measures 135 degrees, then it is obtuse.

B) You are in your favorite class, if your current class is geometry.

2. Rewrite as a conditional in If-then form:

A) All triangles have three sides.

B) An acute angle has a measure between 0 and 90 degrees.

3. Rewrite the bi-conditional statement as a conditional and its converse. A) An angle is right if and only if its measure is 90 degrees.

Conditional: _________________________________________________________________ Converse: ___________________________________________________________________ 4. Write the converse of the statement.

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4. Write the converse of the statement.

The game will be played if it doesn't rain.

5. Write the following as biconditional statements. If it can't be written as biconditional statement, explain. A) If an angle is 150° then is an obtuse angle.

B) If lines are perpendicular then the lines intersect and form a right angle.

6. Create a Venn diagram for the following statements. What conclusion, if any, can be logically deduced? (Hint: Create an if-then statement if necessary) A) If a number is a whole number, then it is an integer. If a number is an integer, then it is a rational number.

B) If an animal if a fish, then it can swim. Jim can swim.

C) Two angles that are complementary have a sum of 90 degrees. Angle K and Angle L are complementary.

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