Discrete Mathematics

Set Operations

Sets - Complement

         

Consider the ground set U={xx is a positive integer less than 33}.U= \{x \mid x \text{ is a positive integer less than } 33\}. If AA is a subset of UU and Ac={xx is a positive integer less than 30},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?A?

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Consider a set UU with 3939 elements. If AA is a subset of UU such that Ac=9, \lvert A^c \rvert =9, how many elements are there in the set A?A?

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

Details and assumptions

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