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Set Operations

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

Complement

         

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 \(A?\)

Details and assumptions

You may choose to read the summary page on Set Notation.

Bella keeps a supply of red, blue, and black pens in a drawer. The drawer has 18 red pens, 18 blue pens, and 11 black pens. If Bella wants a red pen, what is the minimum number of pens she has to pull out from the drawer to make sure she gets a red pen?

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

You may choose to read the summary page on Set Notation.

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