Quiz on If-Then Statements, Logic, Venn Diagramsname ______Pd. ____ Date ____
Quiz on if-then statements, logic, Venn diagramsName ______Pd. ____ Date ____
Multiple Choice Identify the choice that best completes the statement or answers the question./ 1. / What is the converse of the statement “If an angle is acute, then it is not equal to 90°”
A / If an angle is acute, then it is not equal to 90°.
B / If an angle is not acute, then it is equal to 90°.
C / If an angle is equal to 90°, then it is not acute.
D / If an angles is not equal to 90°, then it is acute.
/ 2. / Given the statement “If you lose, then I win”, how is the statement “If I don’t win, then you don’t lose.” related to it?
A / converse
B / inverse
C / contrapositive
D / biconditional
/ 3. / Given the statement “If it barks like a dog, then it’s not a cat.”, how is the statement
“If it does not bark like a dog, then it’s a cat.” related to it?
A / converse
B / inverse
C / contrapositive
D / biconditional
/ 4. / What is the inverse of the statement ~p q?
A / ~q ~p
B / q ~p
C / p ~q
D / ~q p
/ 5. / What is the contrapositive of the statement ~q ~p?
A / p q
B / ~q ~p
C / p ~q
D / ~q p
/ 6. / What is the converse of the statement ~q p?
A / ~q ~p
B / q ~p
C / p ~q
D / ~q p
/ 7. / Let m represent “x is a multiple of four”
Let n represent “x is even”
If x = 10, then which of the following is true?
A / m ^ n
B / ~m ^ ~n
C / ~m ^ n
D / m ^ ~n
/ 8. / Let a represent “x is a multiple of 5”
Let b represent “x is an odd number”
If x = 30, then which of the following is true?
A / a ^ b
B / ~a ^ ~b
C / ~a ^ b
D / a ^ ~b
/ 9. / Let p represent “Sally will not be tardy to class”
Let q represent “Sally has a hall pass”
Which of the following is ~q v p?
A / Sally has a hall pass or Sally will not be tardy to class.
B / Sally will not be tardy to class and Sally has a hall pass.
C / Sally will not be tardy to class or Sally has a hall pass.
D / Sally does not have a hall pass or Sally will not be tardy to class.
/ 10. / Use the Law of Syllogism to determine the conclusion for the following statement:
If two lines are perpendicular, then they form a right angle.
If two lines form a right angle, then they will form four right angles.
A / If two lines are perpendicular, then they will form a right angle.
B / If two lines form a right angle, then the two lines are perpendicular.
C / If two lines are perpendicular, then they will form four right angles.
D / None of the above.
Part II.
Assume p represents the statement “Al will go to a baseball game”, q represents the statement “Al will go to a football game,” and r represents the statement “Al will go to a hockey game.”
1. Write each statement in words.
2. Write each statement using symbols.
a. Al will not go to a hockey game.
b. Al will go to a hockey game or he will go to a baseball game.
c. Al will go to a baseball game and he will not go to a football game.
Part III.
1. Use the Law of Syllogism to make a valid conclusion. If no conclusion can be made, write “none”.
a. If a polygon has three sides, the polygon is a triangle.
If a polygon is a triangle, it will have an angle sum of 180.
Conclusion:
b. If you eat too fast, you will get hiccups.
If you get hiccups, you should drink water upside down.
Conclusion:
c. If it is raining outside, you should carry an umbrella.
If it is cold outside, you should wear a coat.
Conclusion:
Directions: Use the Law of Syllogism to solve the following. (2 points each)
- If then _____.
a. If it is very hot outside, children will go swimming.
Children are going swimming.
Conclusion:
b. If a student takes geometry, he will be very smart.
Bryan takes geometry.
Conclusion:
c. If it rains today, flowers will grow.
It rained today.
Conclusion:
Part IV. Venn Diagrams:
1. Draw a venn diagram using each of the given statements.
a. All vertical angles are congruent angles.
b. All dogs are mammals.
c. In a school, there are 34 students who belong to chess, spirit, and Key clubs. 5 belong to the chess club only, 8 belong to the spirit club only, 3 belong to both the spirit and Key clubs, 4 belong to the chess and spirit club, 2 belong to the Key and chess club, and 6 belong to all three. How many belong to the Key club only?
2. Based on this diagram only, which is a valid conclusion? Circle your choice.
a. No student plays more than one sport.b. No football player also plays baseball.
c. No baseball players also play basketball.
d. No basketball plays also play football.
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