Answer :
Answer:
it is always true
Explanation:
hope it helps
ANSWERS:
The statement "one of every three consecutive positive integers is divisible by 3" is always true.
This is because, among any set of three consecutive positive integers, there will always be at least one integer that is divisible by 3. For example, consider the integers \( n, n+1, \) and \( n+2 \):
- If \( n \) is divisible by 3, then \( n \) itself is divisible by 3.
- If \( n+1 \) is divisible by 3, then \( n+1 \equiv 0 \pmod{3} \), which means \( n \equiv 2 \pmod{3} \).
- If \( n+2 \) is divisible by 3, then \( n+2 \equiv 0 \pmod{3} \), which means \( n \equiv 1 \pmod{3} \).
In each case, one of the integers \( n, n+1, \) or \( n+2 \) will be divisible by 3, ensuring that the statement holds true for any consecutive set of three positive integers.