  ## Identities Contradictions and Conditional Equations

Definition of contradiction. 1 : act or an instance of contradicting the defendant's contradiction of the plaintiff's accusations. 2 a : a proposition, statement, or phrase that asserts or implies both

## Identities, Contradictions and Conditional Equations.

This means that this alternative statement is false, and thus we can conclude that the original statement is true. The statement we are trying to prove must have only two possible

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Contradiction is an equation that is satisfied by some numbers and not by others. Contradiction: is an equation that has no solution.Note: Sometimes equations have no solution. This means ## COLLEGE ALGEBRA

contradiction. 2 (x+3) - 4x + 7. expression. 2 (x+3) - 4x + 7 = -1. equation. No Equal Sign. expression. Equal Sign. equation.

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## 1.1 Linear and Rational Equations

Now that we have an equation to work with, let’s begin to derive a contradiction: √2 = p / q [our assumption] (√2)2 = (p / q)2 [square both sides of the equation] 2 = p2 / q2 2q2 = p2 [multiply