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Subsets

A set $$A$$ is a subset of $$B$$ if all the elements of $$A$$ belong to $$B$$. We write this $$A\subseteq B$$.

The set of mammals is a subset of the set of all animals.

The set of the natural numbers $$\N$$ is a subset of the integers $$\Z$$. But the set $$\Q$$ of the irrational numbers is not.

The set of vowels is a subset of the set of all letters.

$$A$$ is a proper subset if it is a subset different from $$B$$. It contains some elements of $$B$$ but not all of them. We write this as $$A\subset B$$.

$$$ \N\subset\Z,\;\Z\subseteq\Z,\;\{\Tred{A},\Tred{I}\}\subset\{\Tred{A},B,\Tred{I},L\} $$$

The subset of a subset is a subset.

$$$ \N\subset\Z\subset\Q\subset\R$$$
The set of primary colours and the set of secondary colours are both subsets of the set of all colours. They have no elements in common.
The set of primary colours and the set of secondary colours are both subsets of the set of all colours. They have no elements in common.