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Familiarize yourself with the foundational notation, tools and concepts for the operations that are applied to sets.

Consider the ground set \[U= \{x \mid x \text{ is a positive integer less than } 33\}.\] If \(A\) is a subset of \(U\) and \[A^c = \{x \mid x \text{ is a positive integer less than } 30\},\] what is the sum of all the elements in the set \(A?\)

**Details and assumptions**

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Consider a set \(U\) with \(39\) elements. If \(A\) is a subset of \(U\) such that \( \lvert A^c \rvert =9,\) how many elements are there in the set \(A?\)

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How many of the integers from 1 to 100 inclusive are not perfect squares of an integer?

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Consider the set \(U=\{3,5,8,11,15,21\},\) and the subset \(A=\{8,11\}\) of \(U\). What is the sum of all the elements in the set \(A^c?\)

**Details and assumptions**

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