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Geometry – Logic Practice
10/5/09
Name: ______________________________
The Rules:
Conditional:
p q
If it is sunny, then we play outside.
Converse:
q p
If we play outside, then it is sunny.

~ p ~ q
If it is not sunny, then we don’t play outside.

Contrapositive:
~ q ~ p
If we don’t play outside, then it is not sunny.
Inverse:
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 ( p  q)
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 ( p  q)
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: p q
An angle is right if and only if it measures 90 .
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 90 and less than 180.
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 4 x  3  12  2x has exactly one solution.

16. If x 2  36, then x must equal 18 or -18.

17. If mA 122 then the measure of the supplement of A is 58 .
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 30, then it is acute.
 are supplementary, then their sum is 180.
19. .Ic If two angles
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