Conditionals, Converse, Inverse, and Contrapositive
Patterns
Counterexamples
100
Write the conclusion using the Law of Syllogism:
If you do gymnastics, then you are flexible.
If you are flexible, then you can touch your toes.
What is "If you do gymnastics, then you can touch your toes"
100
Is the following a good definition?
A tiger is an animal with stripes
What is "No, because other animals such a zebras have stripes"
100
Is the following conditional True or False?
If a student is in uniform, then they are following the dress code."
What is TRUE
100
Find the next two terms in the sequence:
1, 3, 7, 13, 21
What is "31, 43"
100
If a flower is red, it is a rose.
What is "A carnation can be red, but is not a rose."
200
Write the conclusion using the Law of Syllogism:
If a whole number ends in zero, then it is divisible by 10.
If a whole number is divisible by 10, then it is divisible by 5.
What is "If a whole number ends in zero, then it is divisible by 5"
200
Is the following a good definition?
An obtuse angle is an angle with a measure greater than 90 and less than 180.
What is "Yes"
200
What is the conclusion of the conditional?
If I study for my test, then Ms. Lammers will be happy
What is "Ms. Lammers will be happy"
200
Find the next two terms in the sequence:
0.1, 0.01, 0.001, 0.0001
What is "0.00001, 0.000001"
200
When you multiply a number by 3, it is divisible by 6.
What is "multiply 3 by 5. 15 is not divisible by 3."
300
Write the conclusion using the Law of Detachment:
If there is lightening, then it is not safe to swim.
There is lightening at the pool in Huntsville.
What is "It is not safe to swim at the pool in Huntsville."
300
Write a biconditional for the following conditional:
If you live in Washington, DC, then you live in the capitol of the United States
What is "You live in Washington DC if and only if you live in the capitol of the United States"
300
Write the converse for the following conditional:
If a month has 28 days, then it is February
What is "If the month is February, then it has 28 days"
300
Find the next two terms in the sequence:
7, 13, 19, 25
What is "31, 37."
300
Angles 1 and 2 are supplementary, so one of the angles is acute.
What is "2 right angles"
400
Write the conclusion using the Law of Detachment:
If a figure is a square, then its sides have equal length.
Figure ABCB is a square.
What is "Figure ABCD has sides of equal length"
400
Write a biconditional for the following conditional:
If the figure is a square, then the figure has 4 equal sides
What is "The figure is a square if and only if it has 4 equal sides"
400
Write the inverse for the following conditional:
If a month has 28 days, then it is February
What is "If a month does NOT has 28 days, then it is NOT February"
400
Find the next two terms in the sequence:
1, 4, 9, 16, 25
What is "36, 49"
400
Triangle ABC is a right triangle, so angle A measures 90 degrees.
What is "Angle B or C could be the 90 degree angle"
500
Write the conclusion:
If it is Tuesday, then you eat chicken.
It is Tuesday.
What is "You eat chicken."
500
Write a biconditional for the following conditional:
"If an animal has a long neck, then it is a giraffe"
What is "No biconditional can be written because this is not true. Biconditionals can only be written with true conditionals and true converses"
500
Write the contrapositive for the following conditional:
If a month has 28 days, then it is February
What is "If the month is NOT February, then it does NOT have 28 days."
500
Find the next two terms in the sequence:
1, 2, 6, 24, 120
What is "720, 5040"
500
The difference of two integers is less than either integer.