Consider a set Note that every element in set A is also found in set B, however, the reverse is not true (B contains elements 4, 5 and 6 which are not in A)
Consider another case, Again, we can see that every element in set A is also found in set B and similarly, everything in B cannot be found in set A. B contains negative and odd integers, which are not in A.
To describe this phenomena, mathematicians defined subsets:
Suppose A and B are sets. If every element in A is an element of B, then A is a subset of B and we denote this as
If B is not a subset of A, as in the above cases, then there exists at least one element, say
e.g.1. but since
e.g.3. since and Hint: look at what sets y is in
Every set is a subset of itself :