If A is a positive integer, which of the following must be odd?  Select the correct option:  A) A+1  B) A^2+A  C) A^2+A+1  D) x^2−1  E) 3x^2−3
A. A+1 = can be odd or even. Since O + O =E or E + O = O   B. A^2 + A = A(A+1). Since from the above derivation we already know the term A+1 can be Odd or Even, directly substitute here. A(ODD) = Even (When A is Even) or A(EVEN) = EVEN [When A is ODD]   C. Here's the answer. Since we know the term A^2 + A can always take a EVEN number, EVEN + 1 = ODD   Hence A^2+A+1.
<result>C</result>
If A is a positive integer, which of the following must be odd?