SP20:Lecture 3 prep

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Please come to lecture 3 knowing the following definitions (you can click on the terms or symbols for more information, or you can review the entire lecture notes from last semester here):

Definition: Subset
If [math]A [/math] and [math]B [/math] are sets, then [math]A [/math] is a subset of [math]B [/math] (written [math]A \href{/cs2800/wiki/index.php/%5Csubseteq}{\subseteq} B [/math]) if every [math]x \href{/cs2800/wiki/index.php/%5Cin}{\in} A [/math] is also in [math]B [/math]


Definition: Power set
The power set of a set [math]A [/math] (written [math]\href{/cs2800/wiki/index.php/2}{2}^A [/math])is the set of all subsets of [math]A [/math]. Formally, [math]\href{/cs2800/wiki/index.php/2}{2}^A \href{/cs2800/wiki/index.php/Definition}{:=} \href{/cs2800/wiki/index.php/Set_comprehension}{\{B \mid} B \href{/cs2800/wiki/index.php/%E2%8A%86}{⊆} A\} [/math].
Definition: Union
If [math]A [/math] and [math]B [/math] are sets, then the union of [math]A [/math] and [math]B [/math] (written [math]A \href{/cs2800/wiki/index.php/%5Ccup}{\cup} B [/math]) is given by [math]A \cup B \href{/cs2800/wiki/index.php/Definition}{:=} \{x \href{/cs2800/wiki/index.php/%5Cmid}{\mid} x \href{/cs2800/wiki/index.php/%5Cin}{\in} A \href{/cs2800/wiki/index.php/Or}{\text{ or }} x \href{/cs2800/wiki/index.php/%5Cin}{\in} B\} [/math].
Definition: Intersection
If [math]A [/math] and [math]B [/math] are sets, then the intersection of [math]A [/math] and [math]B [/math] (written [math]A \href{/cs2800/wiki/index.php/%5Ccap}{\cap} B [/math]) is given by [math]A \href{/cs2800/wiki/index.php/%5Ccap}{\cap} B \href{/cs2800/wiki/index.php/Definition}{:=} \{x \href{/cs2800/wiki/index.php/%5Cmid}{\mid} x \href{/cs2800/wiki/index.php/%5Cin}{\in} A \href{/cs2800/wiki/index.php/And}{\text{ and }} x \href{/cs2800/wiki/index.php/%5Cin}{\in} B\} [/math].
Definition: Set difference
If [math]A [/math] and [math]B [/math] are sets, then the set difference [math]A [/math] minus [math]B [/math] (written [math]A \href{/cs2800/wiki/index.php/%5Csetminus}{\setminus} B [/math]) is given by [math]A \href{/cs2800/wiki/index.php/%5Csetminus}{\setminus} B \href{/cs2800/wiki/index.php/Definition}{:=} \{x \href{/cs2800/wiki/index.php/%5Cmid}{\mid} x \href{/cs2800/wiki/index.php/%5Cin}{\in} A \href{/cs2800/wiki/index.php/And}{\text{ and }} x \href{/cs2800/wiki/index.php/%5Cnotin}{\notin} B\} [/math].