Geometry – Logic Practice
Geometry – Logic Practice Name: ______________________________
10/5/09
The Rules:
Conditional: [pic] If it is sunny, then we play outside.
Converse: [pic] If we play outside, then it is sunny.
Inverse: [pic] If it is not sunny, then we don’t play outside.
Contrapositive: [pic] If we don’t play outside, then it is not sunny.
Practice:
1. Conditional: If you don’t brush your teeth, then you get cavities.
Converse:
Inverse:
Contrapositive:
2. Conditional: If it quacks, then it is a duck.
Converse:
Inverse:
Contrapositive:
3. Mark each part of #1 and #2 above with a T for true or a F for false.
4. Put a star next to the logical equivalent of each conditional statement in #1 and #2 above.
The Rules:
Disjunction: p or q [pic] The sun is hot or the moon is made of green cheese.
A disjunction is TRUE if one part is true, or if both parts are true.
A disjunction is FALSE if neither part is true.
Mark each statement “True” or “False”
5. It is October or it is November.
6. You are a cat or your math teacher is Mr. Drix.
7. 4 is even or 8 is prime.
The Rules:
Conjunction: p and q [pic] It is Monday and this is math class.
A conjunction is TRUE only if BOTH parts are true.
A conjunction if FALSE if one part is false or both parts are false.
Mark each statement “True” or “False”
8. Mr. Mills is the principal and Ithaca won the swim meet Friday.
9. Grass is green and the sky is yellow.
10. L comes after M in the alphabet and leaves turn blue in the fall.
The Rules:
Biconditional: [pic] An angle is right if and only if it measures [pic].
Key words: if and only if (abbreviated iff)
True both ways (original statement and its converse).
Exercises:
Rewrite the conditional in “if-then” form:
11. It is time for dinner if it is 6PM.
12. There are 12 eggs if the carton is full.
13. An obtuse angle is an angle that measures more than [pic] and less than [pic].
14. The car runs when there is gas in the tank.
Decide whether the statement is true or false. If false, provide a counterexample.
15. The equation [pic] has exactly one solution.
16. If [pic], then x must equal 18 or -18.
17. If [pic] then the measure of the supplement of [pic] is [pic].
Write the converse of each true statement. If the converse is also true, combine the statements to make a biconditional statement.
18. If an angle measures [pic], then it is acute.
19. .Ic If two angles are supplementary, then their sum is [pic].
20. If an animal is a panther, then it lives in the forest.
Rewrite the biconditional statements as a conditional statement and its converse.
21. Two lines are perpendicular if and only if they intersect to form right angles.
22, A point is a midpoint of a segment if and only if it divides the segment into two congruent segments.
Write a conclusion that can be made given the following pairs of statements.
23. If the light is on, then someone is home. The light is on.
Conclusion:
24. The Liberty Bell is located in Philadelphia, Pennsylvania. Robert has never been to Philadelphia.
Conclusion:
25. Given the true conditional statement “If it is Sunday, then I will watch The Amazing Race”, which statement cannot be true?
a. It is Monday and I will watch The Amazing Race.
b. It is Wednesday and I will not watch The Amazing Race.
c. It is Monday and I will not watch The Amazing Race.
d. It is Thursday and I will watch Survivor.
26. The statement “My favorite ice cream is strawberry or I love snow” is false.
Which of the following statements is true?
a. My favorite ice cream is mint chocolate chip and I don’t like snow.
b. My favorite ice cream is strawberry and I don’t like snow.
c. My favorite ice cream is strawberry and I love snow.
d. My favorite ice cream is mint chocolate chip and I love snow,
Draw the following:
27. adjacent angles 28. Vertical angles
29. supplementary angles 30. Right angle
31. complementary angles 32. Linear pair
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