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Yay testing!!!

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Key Words for Writing Existence Statements

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Key Words for Writing Existence Statements

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Existence - There exists, there is, some, it is possible

Existence Counterexample - There exists a counterexample, original claim (p-->q) is false

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For all, for each, every, if-then, when, there does not exist, only

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Support for and Ways to Write an Existence Claim

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Support for and Ways to Write an Existence Claim

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Present an example - Claim stating there exists an example of [blank].
The Foundation gives an example. Narrative Link demonstrates the example
satisfies the conditions of the claim (is in the claim's domain) and has the desired properties.

Counterexample - Claim the generalization is FALSE or that a counterexample exists.
Foundation gives the counterexample and the Narrative Link demonstrates that the
counterexample satisfies the conditions of the claim but does not satisfy the conclusion.

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Viable Argument Types for Generalizations

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Viable Argument Types for Generalizations

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Variable Argument - A variable is used to represent all cases in the domain of the claim. Foundation must include a variable expression, formula, or equation that illustrates the conditions of the claim and the conclusion. Narrative Link must explain how the expression, formula, or equation is used and that that the conclusion follows from the conditions and must be true.

Exhaustion - ALL possible cases in the domain must be represented. In the Foundation, show that each case in the domain demonstrates the conditions and the conclusions of the claim. Narrative Link states that all cases in the domain have been tested and demonstrate the conclusions of the claim. (This argument type only works with a finite domain.)

Generic Example - The Foundation provides an example in the domain of the claim, and illustrates the conditions of the claim. The Narrative Link explains how the example represents all cases in the domain of the claim. Be explicit about how the properties expressed in the example are shared by ALL cases.

Contradiction - Begin by supposing the claim is FALSE. In the Foundation, express
what it means for the claim to be false. Use logic to develop a false (or absurd) statement, expression, or equation. The Narrative Link tells the reader why the last statement, expression, or equation is absurd and why this shows the original claim must be true.

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A statement that asserts something is true for one particular case (or a few cases).

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A claim that asserts something is true for at least one case in the domain of the claim

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A claim that something is true for all cases in the domain of the claim.