Definition 3.1.23 (Intersections). The intersection \(S_1\cap S_2\) of two sets is defined to be the set $$ S_1\cap S_2:=\{s\in S_1:x\in S_2\}. $$ In other words, \(S_1\cap S_2\) consists of all the elements which belong to both \(S_1\) and \(S_2\). Thus, for all objects \(x\), $$ x\in S_1\cap S_2\iff x\in S_1\text{ and }x\in S_2. $$
Definition 3.1.23
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Exercise 3.4.3
\(\equiv\) { Definition 3.1.23 }