Understanding Subsets in Mathematics: Definition, Examples, and Proper Subsets

subset

In mathematics, a subset refers to a collection of elements that are taken from a larger set

In mathematics, a subset refers to a collection of elements that are taken from a larger set. More precisely, if every element in a set A is also an element in another set B, then A is considered a subset of B, denoted as A ⊆ B.

To illustrate this concept, let’s consider an example. Suppose we have a set A = {1, 2, 3} and another set B = {1, 2, 3, 4, 5}. In this case, we can say that A is a subset of B because every element in A (1, 2, and 3) is also present in B. Mathematically, we can represent this as A ⊆ B.

It’s important to note that a subset can also be equal to the original set. For instance, if we have a set C = {1, 2, 3}, then C is considered a subset of itself, and we write C ⊆ C.

Additionally, there is a concept of a proper subset. A proper subset is a subset that is not equal to the original set. In the example above, if we consider the set C = {1, 2, 3}, then it is both a subset and a proper subset of B because C ⊆ B and C ≠ B.

To summarize, a subset is a set whose elements are all part of another larger set. It is denoted by the symbol ⊆ and can include or equal the original set.

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