Final answer:
The statement is false since the sum of any two odd and consecutive integers will be an integer, not one half.
Step-by-step explanation:
The statement that the sum of two consecutive odd integers is equal to one half is false. To understand this, consider any two consecutive odd integers. Let the first integer be n. Since the integers are consecutive and odd, the next integer would be n+2.
The sum of the two integers would be n + (n+2) which simplifies to 2n+2. To check if this sum can be equal to one half, solve for n: 2n+2 = 1/2, which would imply that n is not an integer, and consequently, the original statement cannot be true since n must be an odd integer.
Another way to look at this is to recognize that the sum of any two integers will always be an integer, therefore, it cannot equal one half, which is not an integer. This understanding is consistent with basic addition properties, where the sum of two integers is always another integer.
The statement 'The sum of two consecutive odd integers is equal to one half' is False.
In order to sum two consecutive odd integers and get one half, we need to examine the properties of odd integers. Odd integers are numbers that cannot be divided evenly by 2. The sum of two consecutive odd integers will always be an even integer. However, one half is not an even integer, so it is not possible for the sum of two consecutive odd integers to be equal to one half.