A set is the mathematical model for a collection of different things. Those things may or may not have something in common.
Therefore, you can define a set by specifying the individual Elements within it, or you can specify it by defining a common feature.
For example, you may say a set consists of a red apple, an orange orange, or a peach peach, or you can say a set consists of information regarding all of the fruits and their colors. Such a set could be denoted F and its components could in this case actually be denoted with two parameters – color, c, and fruit, f.
“True” or “Real” Elements within the set are those which satisfy certain logical statements.
For example, in theory, an apple may be green, red, yellow, or other colors. Likewise, many other fruit may share similar colors.
Therefore, Green Fruits GF a set of all mathematical objects which are both green and are fruits.
This is a subset, created by the intersection of two sets.
Elements f of the set Fruits F which are other colors, belong to the set of Fruits F but not the the set of things that are green in color G.
Likewise, other vegetables (and other objects) which are green are in the set G but only the ones that are also fruits f are within the set GF.
What, therefore, are some of the other elements within GF?
Limes, (Some) Pears, Avocados (at the right stage), (some) Grapes, etc.
