Hello, iPod!
I have to ask: did you write out the sets?
Given: .$\displaystyle \begin{Bmatrix} U &=& \{x\,|\,x\in I,\:20 < x \le 40\} \\ A &=& \{x\,|\,x\text{ is a multiple of 5\}} \\ B &=& \{23,\,33\} \\ C &=& \{x\,|\,x\text{ is prime}\} \end{Bmatrix}$
We have: .$\displaystyle \begin{array}{ccc}U &=& \{21,22,23\,\hdots\,40\} \\ A &=& \{25,30,35,40\} \\ B &=& \{23,\,33\} \\ C &=& \{23,29,31,37\} \end{array}$
List the following sets:
. . $\displaystyle (i)\;B \cap C$ $\displaystyle B \cap C \;=\;\{23,33\} \,\cap\,\{23,29,31,37\} \;=\;\{23\}$
$\displaystyle (ii)\;A \cup B \cup C$
All three sets combined into one set . . .
$\displaystyle A \cup B \cup C \;=\;\{23,25,29,30,31,33,35,37,40\}$
$\displaystyle (iii)\;\overline{A \cup B \cup C}$
This is the complement of the set in part (ii).
$\displaystyle \overline{A \cup B \cup C)} \;=\;\{21,22,24,26,27,28,32,34,36,38,39\}$
$\displaystyle (iv)\;(A \cup B) \cap C $
$\displaystyle (A \cup B) \cap C \;=\;\bigg(\{25,30,35,40\} \,\cup \,\{23,33\}\bigg) \,\cap \,\{23,29,31,37\} $
. . . . . . . . . .$\displaystyle =\;\{23,25,30,33,35,40\} \cap \{23,29,31,37\}$
. . . . . . . . . .$\displaystyle =\;\{23\}$
Shade the following regions.
. . $\displaystyle (i)\;(A \cup B) \cap C$ Code:
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$\displaystyle (ii)\;A \cup (B \cap C)$
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