Which of the following statements is true regarding the expression (a + b) mod n

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Question: Which of the following statements is true regarding the expression (a + b) mod n?

Options:

Correct Answer: It is always equal to (a mod n) + (b mod n)

Solution:

The property of modular arithmetic states that (a + b) mod n = [(a mod n) + (b mod n)] mod n.

Which of the following statements is true regarding the expression (a + b) mod n?

Which of the following statements is true regarding the expression (a + b) mod n?

Step 1: Understand what 'mod' means. 'mod n' means we are looking for the remainder when a number is divided by n.
Step 2: Look at the expression (a + b) mod n. This means we first add a and b together, then find the remainder when that sum is divided by n.
Step 3: Now, consider the expression (a mod n) + (b mod n). This means we find the remainder of a when divided by n, and the remainder of b when divided by n, and then we add those two remainders together.
Step 4: The property of modular arithmetic tells us that if we take the sum of the remainders (from Step 3) and then find the remainder of that sum when divided by n, we will get the same result as in Step 2.
Step 5: Therefore, we can say that (a + b) mod n is equal to [(a mod n) + (b mod n)] mod n.

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