Question

For any positive integer \( q \), every positive integer will be in the form of:

• A. \( q - 1 \)
• B. \( q + 1 \)
• C. \( 2q \)
• D. \( 2q + 1 \)

Hint:

The form \( 2q + 1 \) represents all positive integers because it covers both odd and even numbers by varying \( q \).

Answer 1

The Correct Option is D

Every positive integer can be expressed in the form of \( 2q + 1 \), where \( q \) is any positive integer. This is because: - \( q \) can be any integer, and multiplying it by 2 will always result in an even number. - Adding 1 to an even number will always give an odd number, thus covering all possible positive integers.
Step 1: Conclusion.
Thus, the expression for every positive integer is \( 2q + 1 \).