Patterns and Inductive Reasoning
Conditional Statements
More Statements
Biconditionals and Definitions
Deductive Reasoning
100
What are the next two terms of this sequence?
1, 3, 5, 8, 11, 15, 19, 24...
29, 35
100
Draw a Venn diagram to illustrate the statement.
If you play for the Minnesota Vikings, then you play in the NFL.
100
Is the following conditional statement true or false.
If a figure is a rectangle, then it has exactly four sides.
True
100
Can you write the following statement as a biconditional?
A person who lives in Miami is a person who lives in Florida.
No, you can live in other parts of Florida besides Miami (meaning it is not reversible).
100
If possible, use the Law of Detachment to make a conclusion.
If the light is flashing yellow, then you may drive with caution through the intersection.
The light is flashing yellow.
Then you may drive through the intersection with caution.
200
What are the next two terms in this sequence?
-5, 5, -6, 6, -7, 7, -8,...
8, -9
200
Write a conditional statement that the Venn diagram illustrates.
If a polygon is a rhombus, then the polygon is a quadrilateral.
200
What is the converse of the following conditional statement. Is the converse true or false. If false, provide a counterexample.
If a figure is a rectangle, then it has exactly four sides.
If a figure has exactly four sides, then the figure is a rectangle.
False, rhombus.
200
Write the following true conditional as a biconditional.
If a number is divisible by 2, then the number is even.
A number is divisible by 2 if and only if it is even.
200
If possible, use the Law of Detachment to make a conclusion.
If you swim 100 meters in less than 90 seconds, you will be on the swim team.
Jeremy swam 200 meters in 190 seconds.
No Conclusion
300
Find one counterexample to show that the conjecture is false.
The sum of two integers is always positive.
-5 + 3 = -2
300
Write the sentence as a conditional.
A catfish is a fish that has no scales.
If a fish is a catfish, then the fish has no scales.
300
What is the inverse of the following conditional statement. Is the inverse true or false. If false, provide a counterexample.
If a figure is a rectangle, then it has exactly four sides.
If a figure is not a rectangle, then the figure does not have four sides.
False, rhombus.
300
Write the following true conditional as a biconditional.
If a closed figure is a pentagon, then it has exactly five sides.
A closed figure is a pentagon if and only if it has exactly five sides.
300
If possible, use the Law of Syllogism to make a conclusion.
If two angle measures sum to 180, then the angles are supplementary.
If two angle measures sum to 90, then the angles are complementary.
No Conclusion
400
Find one counterexample to show that the conjecture is false.
All four-sided figures are rectangles.
Parallelogram, Rhombus, Kite, Trapezoid, Square
(any of the answers above)
400
Write the sentence as a conditional.
Purple and yellow are complementary colors.
If two colors are purple and yellow, then they are complementary colors.
400
What is the contrapositive of the following conditional statement. Is the contrapositive true or false. If false, provide a counterexample.
If a figure is a rectangle, then it has exactly four sides.
If a figure does not have four sides, then the figure is not a rectangle.
True
400
Is the following statement a good definition? If not, explain.
A redwood tree is an evergreen tree that grows very tall.
It is not a good definition. Other trees grow very tall and "very" is not precise (it is not reversible).
400
If possible, use the Law of Syllogism to make a conclusion.
If it is Tuesday, then the cafeteria is serving meat loaf.
When the cafeteria serves meat loaf, Harlan brings a sack lunch.
If it is Tuesday, then Harlan brings a sack lunch.