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Logic and Proof

Logic and Proof

Algebraic Proofs Examples

Example 1

Write a proof for the statement "If 2x – 7 = 13, then x = 10." Which properties are used the proof?

Example 2

Find the error in the following "proof" of the statement, "If 3 + z2 = 28, then z = 5." Then, find a counterexample to the statement itself.

StatementsReasons
1. 3 + z2 = 28Given
2. z2 = 25Subtract 3 from both sides of (1)
3. z = 5Square root both sides of (2)

Example 3

Write a proof for the statement "If x3 + y = 10 and 3(3x – 3) = 9, then x = y."

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