Which equation demonstrates the property of the identity element of addition?

The property of the identity element of addition states that when you add zero to any number, the sum is the original number. In this case, the equation demonstrates this property clearly: when zero is added to three, the result is still three. This holds true for all numbers, confirming that zero is the identity element for addition.

Other options may reference other mathematical properties or operations, but they do not illustrate the identity element of addition. For example, adding one to three results in four, while adding three to itself yields six, which do not pertain to the identity property. The subtraction example also does not fit, as it highlights a different operation rather than addition. Therefore, the first equation effectively encapsulates the identity property, making it the correct choice.