Probability
# Set Operations

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 $A?$

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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?

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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