Question

Here is another recursive definition involving integers N and M. Assume 0<=N and 0mod( N, M ) = N, if N < M

mod( N, M ) = mod( N-M, M ), if N >= M
What is the value of mod(2, 5)?

Answer 1

The value of mod(2, 5) is 2, since the first part of the recursive definition applies when N is less than M.

Step-by-step explanation:

The recursive definition provided is for the modulo operation, which is commonly denoted as mod(N, M). This operation finds the remainder when an integer N is divided by another integer M.

Using the provided definition, we need to calculate mod(2, 5). Since 2 is less than 5, we apply the first part of the recursive definition:
mod( N, M ) = N, if N < M. Therefore, mod(2, 5) = 2 because 2 is less than 5.

This is based on the rule that if you're dividing a smaller number by a larger one, the remainder is just the smaller number since the larger one cannot fit into the smaller one even once.