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Inductive Reasoning
Conditional Statements
Deductive Reasoning
Biconditional Statements
Vocabulary
100
The next item in the pattern July, May, March, ...
What is January?
100
The converse of p -> q.
What is q -> p.
100
States: "if p -> q is a true statement and p is true, then q is true."
What is Law of Detachment?
100
Words that are included in a biconditional statement.
What are "if and only if"?
100
The process of reasoning that a rule or statement is true because of specific observations of a pattern.
What is inductive reasoning?
200
The next item in the pattern 1, 10, 18, 25, ...
What is 31?
200
The hypothesis of the conditional statement, "An angle is obtuse if its measure is 107 degrees.
What is its measure is 107 degrees?
200
States, "If p -> q and q -> r are true statements, then p -> r is a true statement."
What is Law of Syllogism?
200
The two statements a biconditional statement combines.
What are conditional and converse?
200
The part of a conditional statement often following the word then.
What is conclusion?
300
The next item in the pattern. -3, 6, -12, 24, ...
What is -48?
300
Write as a conditional statement. A whole number is an integer.
What is "If a number is a whole number, then it is an integer."
300
The following using this kind of reasoning. "To rent a boat, you must take a boating safety course. Jason rented a boat. Jessica concluded that Jason has taken a boating safety course."
What is deductive reasoning? Law of Detachment.
300
The converse for the following conditional statement. "If a triangle is scalene, then its sides have different lengths."
What is "If a triangle has sides of different lengths, then it is scalene"?
300
The process of using logic to draw conclusions from given facts, definitions, and properties.
What is deductive reasoning.
400
Complete the conjecture: The sum of two negative numbers is ______________.
What is negative?
400
Find the truth value of the conditional. If it is false, give a counterexample. "If an angle is acute, then it has a measure of 30 degrees."
What is false. The angle could measure 20 degrees or other value.
400
Given: if a student is in tenth grade, then the student may participate in student council. Eric is a tenth-grader. Conjecture: Eric may participate in student council. The statement is this, based on the Law of Detachment.
What is valid?
400
The truth value of the biconditional statement "A figure is a quadrilateral if and only if it is a polygon." If false, give a counterexample.
What is false, a triangle is a polygon, but not a quadrilateral.
400
Statement formed by both exchanging and negating the hypothesis and conclusion.
What is contrapositive?
500
Determine the truth value, if false give a counter example. If an even number is divided by 2, then the result is an even number.
What is false? Counterexample of 6.
500
Give the inverse of the statement and find the truth value. "If a number is even, then it is divisible by 4."
What is "If a number is not even, then it is not divisible by 4."? True.
500
Given: If a triangle is isosceles, then it has two congruent sides. If a triangle has two congruent angles, then it has two congruent sides. Conjecture: If a triangle is isosceles, then it has two congruent angles. The conjecture is this based on the Law of Syllogism.
What is invalid. Doesn't follow the correct order.
500
The following definition written as a biconditional. Congruent angles have equal measures.
What is "Angles are congruent if and only if they have equal measures"?
500
A statement that describes a mathematical object and can be written as a true biconditional.
What is a definition?