Subsets

Tags

logic

If every element of a set \( A \) is an element of another set \( B \) then \( A \) is a subset of \( B \) (written as \( A \subseteq B \)) and \( B \) is a subset of \( A \) (written as \( B \subseteq of A \)) and hence \( A = B \).

The [see page 32, laws] for subsets are:

• \( \varnothing \subseteq A \).
• \( A \subseteq A \).
• \( A \subseteq B \land B \subseteq C \implies A \subseteq C \).

Sets map conceptually very well to Venn diagrams. They can be used to show the relationships between sets.