Homework 6

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1. (4) AIDM Problem 3.1 on page 129.
2. (8) Let \(U=\{A,B,C,...,Z\}\) (the capital letters of the English alphabet) be the universal set and \(S=\{A, B, C, D\}\).
   1. What is \(|S|\)?
   2. What is \(|P(S)|\)?
   3. How many subsets does \(S\) have?
   4. What is \(|\overline{S}|\)
3. (2) Is \(\mathbb{Z}^+\cup\mathbb{Z}^-=\mathbb{Z}\)? Clearly explain.
4. (8) Let \(A=\{2x | x\in\mathbb{Z}\}\) and \(B=\{3x | x\in\mathbb{Z}\}\). Express each of the following using set notation.
   1. \(A\cup B\)
   2. \(A\cap B\)
   3. \(A\setminus B\)
   4. \(A\times B\)