Conditional Statements
Give me any conditional statement in if-then format.
Examples vary.
If a conditional statement is a -->b, what is the converse symbolized?
b --> a
This organ in the human body is responsible for pumping blood throughout the circulatory system.
The heart
When solving an indirect proof, what do we assume with the original Theorem or conclusion?
We assume the opposite of the original Theorem or conclusion.
What is the symbolization of syllogism?
a-->b
b-->c
a-->c
In a traditional conditional statement what is the a and what is the b when a --> b?
a is the hypothesis
b is the conclusion
If a conditional statement is a -->b, what is the inverse symbolized?
not a --> not b
Who was the person known for organizing Geometry principals?
Euclid
What are we looking for inside of an indirect proof that will prove the original conclusion to be true?
A contradiction.
When the word and definition are in the conditional statement, what are the logically equivalent definitions?
Converse, Inverse, Contrapositive.
What is the vocabulary term for a statement that is assumed to be true without proof?
A postulate
If a conditional statement is a -->b, what is the contrapositive symbolized?
This process in plants uses sunlight to convert carbon dioxide and water into glucose and oxygen.
Photosynthesis
What was the contradiction in the riddle of the Lady and the Tiger?
Is this argument valid or invalid?
When someone makes a 6-7 reference, Mr. Sousa get's frustrated.
Mr. Sousa gets frustrated
Therefore, someone made a 6-7 reference.
Invalid
A theorem
In a direct proof, if we know that
a --> b
b --> c
c --> d
Therefore, what can we assume?
This gas makes up about 78% of Earth's atmosphere.
Nitrogen
In a ____________, an assumption is made at the beginning that leads to a contradiction. The contradiction indicates that the assumption is false and the desired conclusion is true.
An indirect proof.
What is the contrapositive, is it true?
If you live in Maine, then you live in the U.S.
If you do not live in the U.S., then you do not live in Maine, true!
Give me a logically equivalent statement to this conditional statement. Do not use the Contrapositive.
A squatted truck is a truck with a modified suspension that has a significantly raised front end and a lowered rear end, creating a distinct, nose-high "squat" or "lean"
Converse or Inverse
Converse: A truck with a modified suspension that has a significantly raised front end and a lowered rear end, creating a distinct, nose-high "squat" or "lean" is a squatted truck.
Inverse: A non squatted truck is a truck without a modified suspension that has a significantly raised front end and a lowered rear end, creating a distinct, nose-high "squat" or "lean".
If you live in Maine, then you live in the US.
If you live in the US, then you live in North America,
If you live in North America, then you live in the Western Hemisphere.
What is the conclusion we can make from this?
If you live in Maine, then you live in the Western Hemisphere.
This novel by George Orwell features a dystopian society ruled by Big Brother.
1984
In the $1 & $5 envelope demonstration, what was the contradiction that we discovered?
If one of the players had a $5 bill in their envelope, they would have known the other player has $1. Neither knew that the other had a $1 therefore they both had a $1 bill.
Write in "if-then" form.
No calculators are edible.
If it is a calculator, then it is not edible.