Final answer:
The correct answer is A. The sum of two odd integers is even, as proven by direct proof using the standard form of an odd integer (2n + 1). The statement that the sum of two odd integers is even is therefore true.
Step-by-step explanation:
The subject of this question is Mathematics, specifically relating to number theory and probability. The grade level is High School. When dealing with the question of whether the sum of two odd integers is even, we can use a direct proof to show that the statement is true.
An odd integer can be represented as 2n + 1, where n is an integer. If we take two odd integers, say 2n + 1 and 2m + 1, where n and m are both integers, their sum would be (2n + 1) + (2m + 1) = 2n + 2m + 2 = 2(n + m + 1), which is a multiple of 2. Thus, the sum is even, confirming the true option of the original question.
In probability terms, when referring to events such as rolling dice, the probability of compound events such as the intersection (AND) or union (OR) of events A and B is considered. The principle of commutativity (A + B = B + A) is also applicable in calculating the outcome of such events.