Inductive Reasoning & Negations
Conjectures & Counterexamples
Conditionals & Related Conditionals
Biconditionals & Reversible/
Non-reversible
Deductive Reasoning
100
The number that comes next in the sequence: -1, 3, 7, 11, 15, 19... (Use inductive reasoning)
What is 23?
100
The truth value and counterexample (if false) of the following conjecture: "All numbers are odd?
What is false, and 2? What is false, and 8? What is false, and 24?
100
The hypothesis and conclusion of the following conditional statement: "If you hear the tornado siren at 10am on the first Tuesday of the month, then you know it is just a test of the tornado warning system."
What is "you hear the tornado siren at 10am on the first Tuesday of the month (hypothesis), and "you know it is just a test of the tornado warning system" (conclusion)
100
The two statements that must be true for a biconditional statement to be reversible and true.
"What are the "conditional and converse statements"?
100
A valid conclusion using the Law of Detachment when given the following true statements: "If you can dream it, you can do it." "You can dream it."
What is,"you can do it"?
200
The negation of "Points A, B, and C are collinear".
What is "Points A, B, and C are noncollinear"? or What is "Points A, B, and C are not collinear"?
200
The truth value and counterexample (if false) of the following conjecture: "Waukegan High School is located in Illinois."
What is true?
200
The inverse of the conditional statement: "If you live in Waukegan, then you live in the United States".
What is, "If you do not live in Waukegan, then you do not live in the United States?"
200
The converse, and truth value of the converse of the following conditional statement: "If two angles are vertical angles, then they are congruent"
What is, "If two angles are congruent, then they are vertical angles", and false?
200
The valid conclusion using the Law of Syllogism when given the following true statements: "If it is February 14th, then it is Valentine's Day." "If it is Valentine's Day, then I will buy a dozen roses for my mom."
What is "If it February 14th, then I will buy a dozen roses for my mom"?
300
The pattern that gives you the next number in the sequence: -5, 15, -45, 135, ... (Use inductive reasoning)
What is "multiply by -3"?
300
The truth value and counterexample (if false) of the following conjecture: "The product of two prime numbers is always prime."
What is false, and 2 x 3 =6? What is false, and 3 x 5 =15? What is false, and 7 x 9 = 63?
300
The conditional statement of: "All birds can fly".
What is "if an animal is a bird, then it can fly"? or What is "if a creature is a bird then it can fly"?
300
The conditional, and the truth value of the conditional of the following biconditional: "A number is prime if and only if it is divisible by 1 and itself".
What is, "If a number is prime, then it is divisible by 1 and itself" and true?
300
The law that says: if p --> q and q --> r are both true, then p --> r is true.
What is the "Law of Syllogism"?
400
The negation of "Complementary angles do not add up to 90 degrees".
What is, "Complementary angles do add up to 90 degrees"?
400
The truth value and counterexample (if false) of the following conjecture: "Parallel lines intersect to create right angles".
What is false, and "Parallel Lines never intersect"? or What is false, and "Perpendicular lines intersect to create right angles"?
400
The converse of the conditional statement: "If a polygon is a rectangle, then it is a quadrilateral."
What is, "If a polygon is a quadrilateral, then it is a rectangle?"
400
The converse, and truth value of the converse of the following biconditional: "A number is prime if and only if it is divisible by 1 and itself".
What is, "If a number is divisible by 1 and itself, then the number is prime", and true.
400
The conclusion and law used when given the following true statements: If you give a mouse a cookie, then it will ask for a glass of milk. You give a mouse a cookie.
What is "The mouse will ask for a glass of milk", and the Law of Detachment.
500
A false conjecture, and counterexample of your own creation.
What is a "your false conjecture" and "counterexample"?
500
The truth value and counterexample (if false) of the following conjecture: For any integer n, n*n > n
What is false, and 0? What is false, and 1?
500
Identify the hypothesis, conclusion, and contrapositive of the your own conditional statement.
What is "hypothesis", "conclusion", and "contrapositive" of your "conditional statement"
500
The conditional statement, converse statement, and reversible/nonreversible truth value of the following biconditional statement, "Two angles are supplementary if and only if the sum of their measures is 180 degrees".
What is "If two angles are supplementary, then the sum of their measures is 180 degrees" (conditional), "If the sum of the measures of two angles is 180 degrees, then the angles are supplementary" (converse), and reversible/true.
500
The conclusion and law used if you are given these true statements: If a quadrilateral is a square, then it has four right angles. If a quadrilateral has four right angles, then it is a rectangle. If a quadrilateral is a rectangle, then its opposite sides are congruent.
What is, "If a quadrilateral is a square, then it's opposite sides are congruent", using the Law of Syllogism.
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