Set operation (Intersection)

The intersection of sets $A$ and $B$, $A\cap B$, is the set $$ A \cap B = \{ x | x \in A \text{ and } x \in B \} $$

$A\cap B$ consists of elements in both $A$ and $B$.

Venn diagram of $A\cap B$

For example, let $A=\{4,7,8\}and$B = { 10, 4, 9 }. Hence $A\cap B=\{4\}$.

Disjoint

Disjoint sets are sets with no common elements, $A \cap B = \emptyset$.

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Properties of intersection

• The domination law states that $A\cap \varnothing =\varnothing$.
• $A\subseteq B⟺A\cap B=A$