Mathematics: Given the universal set U consisting of all integers between and including 1 and 20, and let the set A consist of all of the powers of 2 (integers of the form 2n where n is a whole number) within the universal set. Find the complement of the set A. Write your answer in proper set notation, for example {1,2,3,4,5,6}.

The number has one six that is in the hundreds place the other one is in the thousand place...

Given the universal set U consisting of all integers

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22.03.2022

$\begin{aligned}\lbrace & \; 3,\, 5,\, 6,\, 7,\, 9,\, 10, \\ &\; 11,\, 12,\, 13,\, 14,\, 15,\, 17, \\ &\; 18,\, 19,\, 20\rbrace\end{aligned}$ .

Step-by-step explanation:

The integer powers of between and are:

$2^{0} = 1$ . $2^{1} = 2$ . $2^{2} = 4$ . $2^{3} = 8$ . $2^{4} = 16$ .

Thus, $A = \lbrace 1,\, 2,\, 4,\, 8,\, 16 \rbrace$ .

The complement of set (denoted as $A^{C}$ ) includes all elements of the universal set that are not in set $A\!$ .

For example, the element is in and is also in . Thus, isn't in $A^{C}$ .

The element is in and isn't in . Thus, is in $A^{C}$ .

Repeat this decision process for each element of to enumerate $A^{C}$ :

$\lbrace 3,\, 5,\, 6,\, 7,\, 9,\, 10, \, 11,\, 12,\, 13,\, 14,\, 15,\, 17, \, 18,\, 19,\, 20\rbrace$ .

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