Final answer:
The statement is true. In property law, the mortgage recorded or registered first usually has priority, this is based on the principle of "first in time, first in right" unless an agreement states otherwise.
Step-by-step explanation:
The statement that in the absence of an agreement to the contrary, the mortgage normally having priority will be the one that was recorded or registered first, based on the principle of "first in time, first in right," is true. This principle is commonly applied in property law and dictates that when multiple parties have claims or interests in the same piece of property, the party whose interest was legally recorded or registered first will have superior rights over those whose interests were recorded or registered later.
In the context of mortgages, this means that if a property is subject to multiple mortgages and there is no prior agreement setting out a different order of priority, the mortgage that was recorded first in the appropriate government office, such as the county recorder's office, will be given preferential treatment in terms of payoff from the proceeds of a sale or foreclosure of the property.