Term
conditional statement
(or conditional) |
|
Definition
|
A statement that can be written in the form
"if _____ then _____," where the first blank is the hypothesis and second blank is the conclusion.
Example: "If an animal is an ape, then the animal has opposable thumbs and no tail." |
|
|
Term
|
Definition
The phrase following the word "if" in a conditional statement.
Example: "If an animal is an ape, then the animal has opposable thumbs and no tail." In this conditional "animal is an ape" is the __________. |
|
|
Term
|
Definition
The phrase following the word "then" in a conditional statement.
Example: "If an animal is an ape, then the animal has opposable thumbs and no tail." In this conditional "animal has opposable thumbs and no tail" is the __________.
|
|
|
Term
| deductive reasoning (deduction) |
|
Definition
The process of drawing conclusions by using logical reasoning in an argument.
Example
- If a parallelogram has four right angles, then the parallelogram is a rectangle.
- A square is a parallelogram with four right angles.
- Therefore a square is a rectangle.
|
|
|
Term
converse
(or converse of a conditional) |
|
Definition
The statement formed by switching the hypothesis and conclusion of a conditional statement to form a new conditional statement.
Example: Given the conditional "If an animal is an ape, then the animal has opposable thumbs and no tail,” the __________ would be "If an animal has opposable thumbs and no tail, then the animal is an ape."
|
|
|
Term
|
Definition
An example that proves that a statement, often a conjecture, is false.
Example: Given the statement "If an animal is human, then it is a man," a __________ would be ... a woman! |
|
|
Term
|
Definition
A series of logically linked conditional statements. They are linked because the conclusion of one statement is the hypothesis of the next.
Example:
If it is Fall in Oregon, it is raining.
If it is raining, then I stay inside.
If I stay inside, then I get my homework done.
So ... If it is Fall in Oregon, then I get my homework done. |
|
|
Term
|
Definition
A statement using "if and only if."
Example: "A polygon is a triangle if and only if it has three sides." This __________ means the same thing as the following two conditionals:
"If a polygon is a triangle, then it has three sides."
"If a polygon has three sides, then it is a triangle." |
|
|
Term
Euler diagram
(or Venn diagram) |
|
Definition
A diagram that shows the logical relationships among a number of sets. |
|
|
