Term
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Definition
| Statement: A sentence that is either true or false, but not both. |
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Term
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Definition
| Reasoning: the step by step process that begins with a known fact or assumption and builds to a conclusion in an orderly, concise manner. This is also known as logical thinking. |
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Term
| What is the notation for negating a statement? |
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Definition
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Term
| What is the notation for the universal quanitfier? |
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Definition
An upside down capital A (pg 167 in text) |
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Term
What is the notation for the existential quantifier? |
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Definition
A capital backwards E (pg 167 in text) |
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Term
| An argument that displays good reasoning without regard to the truth of its statements |
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Definition
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Term
| The concluding statement of a discussion together with the statements that were intended as reasons for it |
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Definition
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Term
| Review how to negate statements that contain a quantifier and statements that do not contain a quantifier. |
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Definition
To negate statements that contain a quantifier you must do 2 things:
1)Negate the sentence
and
2) Switch to the opposite quantifier
See section 5.2 and review the chart we went over in class |
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Term
Negate the following statement:
All men are sinners. |
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Definition
| Some men are not sinners. |
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Term
Negate the following statement:
Some pies are not cherry. |
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Definition
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Term
Negate the following statement:
There is at least one purple flower. |
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Definition
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Term
Negate the following sentence:
Some days are better than others. |
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Definition
| No days are better than any other days. |
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Term
Practice writing conditional statements.
Example, Write the following as a conditional statement:
There are no clouds in the sky, so it is not raining. |
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Definition
| If there are no clouds in the sky, then it is not raining. |
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Term
| Know how to tell if a sentence is a statement and if it is true or false. |
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Definition
| Look at section 5.2, A excercises |
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Term
| What types of sentences in the English language are never statements? |
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Definition
| Interrogative and imperative |
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Term
| Practice writing the inverse, converse and contrapositive of conditional statements. (section 5.4) |
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Definition
Converse- switch the hypothesis and the conclusion (the "p" and "q")
Inverse- negate both the hypothesis and the conclusion
Contrapositive- the inverse of the converse (switch the hypothesis and the conclusion and negate both) |
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Term
Write the converse of the following statement:
"If we have a blizzard, then school will be canceled." |
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Definition
| "If school is canceled, then we had a blizzard." |
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Term
Write the inverse of the following statement:
"If we have a blizzard then school will be canceled." |
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Definition
| "If we do not have a blizzard, then school will not be canceled." |
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Term
Write the contrapositive of the following statement:
"If we have a blizzard, then school will be canceled." |
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Definition
| "If school is not canceled, then we did not have a blizzard." |
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Term
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Definition
| A proof is a system of reasoning or argument to convince a person of the truth of a statement |
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Term
| What is the difference betwen inductive and deductive reasoning? |
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Definition
Inductive reasoning: an argument to establish that a statement is probably true.
Deductive reasoning: an argument to establish that a statement is absolutely certain |
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Term
| An argument is ____________________ if the reasoning proceeds logically from the premises to the conclusion. |
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Definition
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Term
| An argument is ______________ if it is valid and the premises are true. |
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Definition
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Term
| Can an argument be sound if it is invalid? |
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Definition
| NO. If the argument is invalid it cannot be sound. |
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