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Universal set
The set of all elements being considered in a given situation, usually drawn as a rectangle and often labelled $U$.
Subset
A set $A$ is a subset of $B$ (written $A\subseteq B$) if every element of $A$ is also an element of $B$.
Venn diagrams are named after the English mathematician John Venn, who popularized this way of representing logical relationships.
When you learn Venn diagrams, it helps to connect each symbol to a visual idea.
Set intersection
The set of elements that are in both sets. For sets $A$ and $B$, the intersection is $A \cap B$.
Union
The set of elements that are in at least one of the sets. For sets $A$ and $B$, the union is $A \cup B$.
Complement
The set of elements not in a set. The complement of $A$ (relative to $U$) is $A'$.
The overlap of the circles is shaded for $A \cap B$ because an element must satisfy both conditions: it is in $A$ and in $B$.
For $A \cup B$ you shade all of circle $A$ and all of circle $B$. The "or" here is inclusive, so elements in the overlap count too.
In set language, "$A$ or $B$" usually means inclusive or: elements in $A \cap B$ are included in $A \cup B$.
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Paywall
(on a website) an arrangement whereby access is restricted to users who have paid to subscribe to the site.
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