# Chapter 6 - Review - Review Exercises: 9

($P\cap E^{\prime}\cap Q)^{\prime}$

#### Work Step by Step

$A^{\prime}$ is the complement of A (in $S$), the set of all elements of $S$ NOT in $A$. $A^{\prime}=\{x\in S|x\not\in A\}$ For an element to be in $A\cup B$, it must be in $A$ OR in $B$. For an element to be in $A\cap B$, it must be in $A$ AND in $B$. ---------------- S: the set of all integers; P: the set of all positive integers E: the set of all even integers; Q: the set of all integers that are perfects squares -------------- The set of all integers that are not positive odd perfect squares NOT [ (positive) AND (Odd) AND (perfect squares)] NOT [ (from P) AND (NOT from E) AND ( from Q) ] ($P\cap E^{\prime}\cap Q)^{\prime}$

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