Conditionals
The short form notation for an 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?
What does inductive reasoning depend on to make conclusions?
Patterns
What postulate is shown below:
a = c
a + b = c + b
Addition Postulate of Equality
What statements generally go at the beginning of a proof?
The short notation 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.
Two Column Proofs
This form of a proof is useful for showing how previous steps are related.
What is a flowchart proof?
Rewrite "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?
When doing a flowchart proof, what does the arrow tell you?
The statement the arrow is going to is a conclusion from the statement the arrow is coming from.
These types of angles are useful in proofs as they are always congruent.
What are vertical angles.
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.
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."
False
Determine the truth value of the biconditional statement: "You are in geometry if and only if you are in math class."
False, if you break it into "If you are in math class, then you are in geometry." Algebra 1 is a counterexample.
You can connect any three points to form a triangle. True or false, if false give a counterexample.
What is the statement disproved by 3 collinear points?
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?"
This property states that if a = b and b = c, then a = c.
What is the transitive property.