Counterexamples
Compound Statements
Conditional Statements
Deductive Reasoning
100
True or False. If false, provide a counterexample.
The sum of any two consecutive integers is always odd.
True
100
Write the following compound statement using the statements below. Then determine the truth value.
Write p V q.
Points C, E, and B are collinear or angle AEC is congruent to angle DEB.
True
100
Write in if-then form.
Those that finish the marathon will get a medal.
If you finish the marathon, then you will get a medal.
100
Determine if the following argument is valid or invalid. If valid state the law (Detachment, Syllogism, Contrapositive).
Given: If you go camping, then you will need a flashlight.
Given: If you need a flashlight, then you will need extra batteries.
Conclusion: If you go camping, then you will need extra batteries.
Valid
Syllogism
200
True or False. If false, provide a counterexample.
If a x b = 0, then either a = 0 or b = 0.
False
a = 0 and b = 0
200
Write the following compound statement using the statements below. Then determine the truth value.
Write ~p ꓥ r.
Points C, E, and B are not collinear and ray EF is the angle bisector of angle AED.
True
200
Identify the hypothesis and conclusion.
If it is daylight saving time, then I must reset my clocks.
Hypothesis: it is daylight saving time
Conclusion: I must reset my clocks
200
Determine if the following argument is valid or invalid. If valid state the law (Detachment, Syllogism, Contrapositive).
Given: If you leave the country, then you will need a passport.
Given: Nate is planning a trip to Italy.
Conclusion: Nate will need a passport.
Valid
Detachment
300
True or False. If false, provide a counterexample.
The product of two numbers is always larger than either number.
False
0 x 2 = 0
0 > 2 false
0 > 0 false
300
Write the following compound statement using the statements below. Then determine the truth value.
Write r V ~ s.
Ray EF is the angle bisector of angle AED or angle BEC is not an acute angle.
True
300
Write the contrapositive.
If a number is a natural number, then it is also a whole number.
If a number is not a whole number, then it is not a natural number.
300
Determine if the following argument is valid or invalid. If valid state the law (Detachment, Syllogism, Contrapositive).
Given: If the sum of the measures of two angles is 180, then they are supplementary.
Given: Angle D = 110 and angle E = 70
Conclusion: Angle D and angle E are supplementary angles.
Valid
Detachment
400
True or False. If false, provide a counterexample.
Dividing by 2 always produces a number less than the original number.
False
-2/2=-1
-1<-2 false
400
Write the following compound statement using the statements below. Then determine the truth value.
Write ~q ꓥ ~r.
Angle AEC is not congruent to angle DEB and ray EF is not the angle bisector of angle AED.
False
400
Write the biconditional.
If a number is a natural number, then it is also a whole number.
A number is a natural number if and only if it is a whole number.
400
Determine if the following argument is valid or invalid. If valid state the law (Detachment, Syllogism, Contrapositive).
Given: If you buy one pair of shoes, then you get another pair for 50% off.
Given: Carolyn does not buy a pair of shoes.
Conclusion: Carolyn does not get another pair for 50% off.
Invalid
Inverse Error
500
True or False. If false, provide a counterexample.
Vertical angles are never complementary angles.
False
500
Write the following compound statement using the statements below. Then determine the truth value.
Write ~r V ~s.
Ray EF is not the angle bisector of angle AED or angle BEC is not an acute angle.
True
500
p: you have a library card
q: you can check out books
Write ~p → ~q.
Identify the if-then statement as the converse, inverse, contrapositive, or biconditional.
If you do not have a library card, then you cannot check out books.
Inverse
500
Determine if the following argument is valid or invalid. If valid state the law (Detachment, Syllogism, Contrapositive).
Given: If Sally goes to the airport, then she will need to pay for parking.
Given: Sally does not pay for parking.
Conclusion: Sally does not go to the airport.
Valid
Contrapositive