Subset facts for kids
A subset is like a smaller group of things taken from a bigger group. Imagine you have a big box of all your toys. If you pick out just your action figures, that smaller group of action figures is a subset of all your toys.
In set theory, a subset is a set (which is just a collection of things) where every item in the smaller set is also in the bigger set. The bigger set is called a superset.
For example, if Set A is {apple, banana} and Set B is {apple, banana, orange, grape}, then Set A is a subset of Set B because both apple and banana are in Set B.
If a subset has *some* but not *all* of the items from the bigger set, it's called a proper subset. Using our toy example, your action figures would be a proper subset of all your toys, because you still have other toys like cars or building blocks.
We use special symbols to show if one set is a subset of another:
- The symbol ⊆ means "is a subset of". It means the smaller set can have some or all of the items from the bigger set. It can even be exactly the same set.
- The symbol ⊂ means "is a proper subset of". This means the smaller set has fewer items than the bigger set. It cannot be exactly the same set.
The symbols ⊃ and ⊇ are the opposite. They mean the first set is a (proper) superset of the second.
Examples of Subsets
Let's look at some examples to make it clearer:
- Imagine you have a set of numbers: {1, 2, 3}. This set is a proper subset of {-563, 1, 2, 3, 68}. This is because all the numbers (1, 2, 3) are in the bigger set, but the bigger set has more numbers.
- Think about all the real numbers (which include all numbers you can think of, like 0.5, -7, pi, etc.). The numbers between 0 and 1 (including 0 and 1) form a proper subset of all real numbers. We can write this as:
[0, 1] ⊂ R This means the set of numbers from 0 to 1 is a proper subset of all real numbers.
- A set can also be a subset of itself. For example, {46, 189, 1264} is a subset of {46, 189, 1264}. This is because all elements in the first set are also in the second set. We write this as:
{46, 189, 1264} ⊆ {46, 189, 1264}
- This same set {46, 189, 1264} is also a proper subset of the natural numbers (which are 1, 2, 3, and so on). This is because 46, 189, and 1264 are all natural numbers, but there are many more natural numbers not in this small set. We write this as:
{46, 189, 1264} ⊂ N
Related Topics
