subset (original) (raw)

Given two sets A and B, we say that A is a subset of B (which we denote as A⊆B or simply A⊂B) if every element of A is also in B. That is, the following implication holds:

The relation between A and B is then called set inclusion.

Some examples:

The set A={d,r,i,t,o} is a subset of the set B={p,e,d,r,i,t,o} because every element of A is also in B. That is, A⊆B.

On the other hand, if C={p,e,d,r,o}, then neither A⊆C (because t∈A but t∉C) nor C⊆A (because p∈C but p∉A). The fact that A is not a subset of C is written as A⊈C. Similarly, we have C⊈A.

If X⊆Y and Y⊆X, it must be the case that X=Y.