Chapter 1 Section 1

Notes

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Linguistic Mapping Exercises

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Knowledge Checks

1. Explicitly write down all the elements of the set \(S\) given by \[S=\{n\in\mathbb{N}\colon 2n\leq 8\}.\]

2. Take \(A\) and \(B\) to be the sets given by \[A=\{-1,1\}\quad\text{and}\quad B=\{-1,0,1\}.\] Determine whether the following statements are true or false.

   1. \(A\subseteq B\)
   2. \(B\subseteq A\)

3. Take \(A\), \(B\) and \(C\) to be the sets given by \[A=\{-1,1\},\quad B=\{-1,0,1\}\quad\text{and}\quad C=\{0,1,5,6\}.\] Determine whether the following statements are true or false.

   1. \(A\subseteq B\)
   2. \(B\subseteq A\)
   3. \(C\subseteq A\)
   4. \(B\subseteq C\)
   5. \(C\subseteq B\)

4. Take \(A\) and \(B\) to be the sets given by \[A=\{-2,-1,0,1,4\}\quad\text{and}\quad B=\{-1,0,1,3\}.\] Write out explicitly all elements.

   1. \(A\cup B\)
   2. \(A\cap B\)

5. Determine the following intersection: \[\{1\}\cap\{-1,0\}.\]

6. Take \(X\), \(Y\) and \(Z\) to be the sets given by \[X=\{x\in\mathbb{N}\colon x\text{ is even}\},\quad Y=\{y\in\mathbb{N}\colon y<21\}\quad\text{and}\quad Z=\{z\in\mathbb{N}\colon z\text{ is a multiple of }3\}.\] Determine \[Z\cap(X\cap Y).\]

7. Take \(A\) and \(B\) to be the sets given by \[A=\{-2,-1,0,1,2\}\quad\text{and}\quad B=\{-3,-1,0,3\}.\] Determine the following.

   1. \(A\smallsetminus B\)
   2. \(B\smallsetminus A\)

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Practice Problems

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