The principle of crosscutting relationships states that fossil organisms succeeded one another through time in a definite and recognizable order and that the relative ages of rocks can therefore be recognized from their fossils

The statement is false. The Principle of faunal succession is the one that states that fossil organisms succeeded one another through time in a definite and recognizable order and that the relative ages of rocks can therefore be recognized from their fossils.

Explanation:

The principle of faunal succession establishes that the fossils contained in a stratum are from the time in which it was formed; therefore, two strata that have the same fossils are of the same antiquity. The strata that were deposited in different geological epochs contain different fossils, due to the continuous and irreversible nature of biological evolution. In other words, rocks are formed in a particular geological time interval and can be distinguished and identified by their fossil content from other rocks formed in another time interval, this is known as the law of faunal succession.

The principle of crosscutting states that if a rock body cuts to another it is younger than the cut body, this principle of geology allows igneous rock bodies to be related, an igneous intrusion is always younger than the rock it cuts.