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Conditionals
Biconditionals
Inductive Reasoning and Counterexampels
Deductive Reasoning
Theorems and Properties
100
The representation for a inverse statement.
What is "~p -> ~q?"
100
The type of conditional that you combine with the original "If-then" statement to make a biconditional.
What is the converse?
100
reasoning based on patterns
What is Inductive Reasoning
100
the process of reasoning logically f rom given statements or facts to a conclusion.
What is deductive reasoning?
100
Vertical Angles Theorem
What is the theorem that states that vertical angles are congruent?
200
The representation for a contrapositive statement.
What is "~q -> ~p?"
200
The statement that you use to connect a conditional with its converse to make a biconditional.
What is "if and only if?"
200
1, 5, 10, 15, 20, 25,...
What is a sequence with a pattern that starts with 1 and finds the next number by multiplying the previous number by 5?
200
It allows you to state a conclusion from two true conditional statements when the conclusion of one statement is the hypothesis of the other statement.
What is the Law of Syllogism?
200
a(b+c)=ab+ac
What is the distribution property.
300
"The sky is blue." as a conditional.
What is "If it is the sky, then it is blue?"
300
The two statements "If I am breathing, then I am alive" and "If I am alive, then I am breathing" put together in a biconditinal.
What is "I am breathing if and only if I am alive?"
300
The 25th term in the following sequence: Circle, Star, Rectangle, Circle, Star,...
What is a circle?
300
Gives you one "if-then" statement and a statement that tells you that the "if" statement is true.
What is the Law of Deduction?
300
Angle A is congruent to Angle A
What is the Reflexive Property of Congruence?
400
The contrapositive of "If it is a dog, then it is an animal."
What is "If it is not an animal, then it is not a dog?"
400
"In the U.S., if it is July 4, then it is Independence Day." rewritten as a biconditional
What is "In the U.S., it is July 4 if and only if it is Independence Day?"
400
If the name of a month starts with the letter J, it is a summer month.
What is a statement that is disproved by the counterexample "January?"
400
The conclusion from the following: "All national parks are interesting. Mammoth Cave is a national park."
What is "Mammoth Cave is interesting?"
400
If a=b and b=c, then a=c.
What is the transitive property of equality.
500
The converse of "I wear my socks if I wear tennis shoes."
What is "If I wear socks, then I wear tennis shoes."
500
The two statements that form the biconditional "A ray is an angle bisector if and only if it divides an angle into two congruent angles."
What is "If a ray is an angle bisector, then it divides an angle into two conrguent angles." and "If a ray divides an angle into two congruent angles, then it is an angle bisector?"
500
You can connect any three points to form a triangle.
What is the statement disproved by 3 collinear points?
500
The conclusion from the following: "If I am out in the sunshine, then I am happy. If I can go to the park, then I am out in the sunshine."
What is "If I can go to the park, then I am happy?"
500
AB + BC = BC + AB
What is the Symmetric Property of Equality.