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Understanding Basic Algebraic Equations and Functions in Z8

This article explores fundamental concepts of algebra within the Z8 mathematical structure. It presents a series of simple arithmetic problems such as 3 + 4 and 5 + 7, leading to an understanding of modular arithmetic. The content includes solving equations like x + 5 = 1 and x * 3 = 1, highlighting cases where no solution exists. Additionally, the discussion delves into determining whether various relations are functions, providing a clear Yes or No answer for each example discussed. Perfect for learners seeking foundational knowledge in algebra.

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Understanding Basic Algebraic Equations and Functions in Z8

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  1. InZ8, what is 3 + 4? 1 2 3 4 5 6 7 8 9 0

  2. InZ8, what is 5 + 7? 1 2 3 4 5 6 7 8 9 0

  3. InZ8, what is 5  5? 1 2 3 4 5 6 7 8 9 0

  4. InZ8, solve the equation: x + 5 = 1. We get x = • 2 3 4 5 6 7 8 9 • 0 = No solution.

  5. InZ8, solve the equation: x  3 = 1. We get x = • 2 3 4 5 6 7 8 9 • 0 = No solution.

  6. InZ8, solve the equation: x  4 = 1. We get x = • 2 3 4 5 6 7 8 9 • 0 = No solution.

  7. Is the relation in Example 7a a function? 1. Yes 2. No

  8. Is the relation in Example 7b a function? 1. Yes 2. No

  9. Is the relation in Example 7c a function? 1. Yes 2. No

  10. Is the relation in Example 7d a function? 1. Yes 2. No

  11. Is the relation in Example 7e a function? 1. Yes 2. No

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