Conditionals
The representation for a inverse statement.
What is "~p -> ~q?"
The type of conditional that you combine with the original "If-then" statement to make a biconditional.
What is the converse?
reasoning based on patterns
What is Inductive Reasoning
the process of reasoning logically from given statements or facts to a conclusion.
What is deductive reasoning?
What statements generally go at the beginning of a proof?
An educated guess from incomplete information or a pattern
hypothesis
The representation for a contrapositive statement.
What is "~q -> ~p?"
The statement that you use to connect a conditional with its converse to make a biconditional.
What is "if and only if?"
Odd.
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?
What are supplementary angles
Add up to 180 degrees
An if-then statement
conditional statement
"The sky is blue." as a conditional.
What is "If it is the sky, then it is blue?"
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?"
The 25th term in the following sequence: Circle, Star, Rectangle, Circle, Star,...
What is a circle?
Gives you one "if-then" statement and a statement that tells you that the "if" statement is true.
What is the Law of Deduction?
What type of angles are always congruent
What are vertical angles.
When you switch the "if" with the "then"
converse
The contrapositive of "If it is a dog, then it is an animal." and its truth value.
What is "If it is not an animal, then it is not a dog?"
True
"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?"
If the name of a month starts with the letter J, it is a summer month. True or False, if false give a counterexample.
What is a statement that is disproved by the counterexample "January?"
The conclusion from the following: "All national parks are interesting. Mammoth Cave is a national park."
What is "Mammoth Cave is interesting?"
What property is being show: a(b+c)=ab+ac
What is the distribution property.
When you negate the 'if' and 'then' statements
inverse
Write the converse of "If I wear tennis shoes, then I wear socks" and its truth value.
What is "If I wear socks, then I wear tennis shoes."
True
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?"
Make a conjecture about the sum of three consecutive integers
The answer is the middle number times 3
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?"
Prove: 2x+3=13
2x+3=13 Given
2x=10 SPE
x=5 DPE
When you switch the 'if' and 'then' statements, and negate them
Contrapositive