91Ó°ÊÓ

Let \(A=\\{a, e, f, g, i\\}, B=\\{b, d, e, g, h\\}, C=\\{d, e, f, h, i\\},\) and \(U=\\{a, b, \ldots, k\\}.\) Find each set. $$(A-B)-C$$

Let \(A\) and \(B\) be two sets such that \(|A|=2 a-b,|B|=2 a,|A \cap B|=a-b\) and \(|U|=3 a+2 b .\) Find the cardinality of each set. Find \(|A|\) if \(|A|=|B|,|A \cup B|=2 a+3 b,\) and \(|A \cap B|=b.\)

In Exercises \(7-10,\) identify the set S that is defined recursively. $$ \begin{array}{l}{\text { i) } 2 \in S} \\ {\text { ii) } x, y \in S \rightarrow x \pm y \in S}\end{array} $$

Identify the set S that is defined recursively. i) \(2 \in S\) ii) \(x, y \in S \rightarrow x \pm y \in S\)

In Exercises \(7-10,\) identify the set S that is defined recursively. $$ \begin{array}{l}{\text { i) } \emptyset \in S} \\ {\text { ii) } x \in X, A \in S \rightarrow\\{\mathrm{x}\\} \cup A \in S}\end{array} $$

Let \(A\) and \(B\) be two sets such that \(|A|=2 a-b,|B|=2 a,|A \cap B|=a-b\) and \(|U|=3 a+2 b .\) Find the cardinality of each set. Find \(|A \cap B|\) if \(|A|=a+b=|B|\) and \(|A \cup B|=2 a+2 b.\)

Let \(A=\\{a, e, f, g, i\rangle, B=\\{b, d, e, g, h\\}, C=\\{d, e, f, h, i\\},\) and \(U=\\{a, b, \ldots, k\\}\) Find each set. $$ A-(B-C) $$

Let \(A=\\{a, e, f, g, i\rangle, B=\\{b, d, e, g, h\\}, C=\\{d, e, f, h, i\\},\) and \(U=\\{a, b, \ldots, k\\}\) Find each set. $$ (A \cup B)-C $$

Find \(|A \cap B|\) if \(|A|=2 a,|B|=a,\) and \(|A \cup B|=2 a+b\).

Using the sets \(A=\\{a, b, e, h\\}, B=\\{b, c, e, f, h |, C=\\{c, d, f, g\\}, \text { and }\) \(U=\\{a, \ldots, h\\},\) find the binary representation of each set. $$ A \cap B $$