How are the laws of superposition and crosscutting relationships used to determine the relative ages of rock?

By using superposition and cross cutting relationships, geologists can determine relative ages of rocks. This means they can determine which rocks are older and which are younger, but not the exact ages of the rocks. 

The law of superposition states that the rocks at the bottom of an undisturbed sequence of layers are older than the rocks above them. The rocks at the bottom had to have been there before the rocks on top of...

By using superposition and cross cutting relationships, geologists can determine relative ages of rocks. This means they can determine which rocks are older and which are younger, but not the exact ages of the rocks. 

The law of superposition states that the rocks at the bottom of an undisturbed sequence of layers are older than the rocks above them. The rocks at the bottom had to have been there before the rocks on top of them could be deposited. A great example of this can be seen at the Grand Canyon. As you hike down the canyon, you walk by many different rock layers, and the rocks get older and older as you walk down. It is like going back in time through millions of years of geologic history. 

Cross cutting relationships help geologists use geologic features such as faults and intrusions along with rock layers to determine which layers and features are oldest and which are youngest. Again, geologists can determine relative ages, but not exact ages using this method. The principle of cross cutting relationships states that geologic features that cut through other features are younger than the features they cut through. An example would be a fault that cuts through some layers of rocks. Those layers of rock had to be there before the fault could cut through them, so the fault is younger and the rock layers are older (with the layers on the bottom being the oldest by the law of superposition). In the diagram below, we can use cross cutting relationships to determine that the volcanic dike D is younger than A, B, and C because it cuts through them. The rock layer E is younger than D because it cuts through D and is the top layer of rock.