Which of the following equations represents a valid modular arithmetic statement

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Question: Which of the following equations represents a valid modular arithmetic statement?

Options:

Correct Answer: 5x ≡ 10 (mod 5)

Solution:

All options are valid, but 5x ≡ 10 (mod 5) simplifies to 0 ≡ 0, which is trivially true.

Which of the following equations represents a valid modular arithmetic statement?

Which of the following equations represents a valid modular arithmetic statement?

Step 1: Understand what modular arithmetic means. It involves equations where numbers wrap around after reaching a certain value, called the modulus.
Step 2: Look at each equation provided in the options to see if they follow the modular arithmetic rules.
Step 3: Check if each equation can be simplified or if it holds true under the modulus specified.
Step 4: For the equation 5x ≡ 10 (mod 5), simplify it by dividing both sides by 5. This gives you x ≡ 2 (mod 1).
Step 5: Realize that any number is congruent to 0 modulo 1, so this simplifies to 0 ≡ 0, which is always true.
Step 6: Conclude that while all options may be valid, the equation 5x ≡ 10 (mod 5) simplifies to a trivial truth.

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