# 14.4: Sets

$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$

$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$

$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$

( \newcommand{\kernel}{\mathrm{null}\,}\) $$\newcommand{\range}{\mathrm{range}\,}$$

$$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$

$$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$

$$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$

$$\newcommand{\Span}{\mathrm{span}}$$

$$\newcommand{\id}{\mathrm{id}}$$

$$\newcommand{\Span}{\mathrm{span}}$$

$$\newcommand{\kernel}{\mathrm{null}\,}$$

$$\newcommand{\range}{\mathrm{range}\,}$$

$$\newcommand{\RealPart}{\mathrm{Re}}$$

$$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$

$$\newcommand{\Argument}{\mathrm{Arg}}$$

$$\newcommand{\norm}[1]{\| #1 \|}$$

$$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$

$$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$

$$\newcommand{\vectorA}[1]{\vec{#1}} % arrow$$

$$\newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow$$

$$\newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$

$$\newcommand{\vectorC}[1]{\textbf{#1}}$$

$$\newcommand{\vectorD}[1]{\overrightarrow{#1}}$$

$$\newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}}$$

$$\newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}}$$

$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$

$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$

1. $$\{m, i, s, p\}$$ 3. One possibility is: Multiples of 3 between 1 and 10

5. Yes 7. True

9. True 11. False

13. $$A \cup B=\{1,2,3,4,5\}$$ 15. $$A \cap C=\{4\}$$

17. $$A^{c}=\{6,7,8,9,10\}$$ 19. $$D^{c} \cap E=\{t, s\}$$

21. $$(D \cap E) \cup F=\{\mathrm{k}, \mathrm{b}, \mathrm{a}, \mathrm{t}, \mathrm{h}\}$$ 23. $$(F \cap E)^{c} \cap D=\{\mathrm{b}, \mathrm{C}, \mathrm{k}\}$$

25. 27.

29. One possible answer: $$(A \cap B) \cup(B \cap C)$$

31. $$\left(A \cap B^{2}\right) \cup C$$ 33. $$5$$

35. $$6$$ 37. $$\mathrm{n}(A \cap C)=5$$

39. $$\mathrm{n}(A \cap B \cap C)=3$$ 41. $$\mathrm{n}(G \cup H)=45$$

43. 136 use Redbox

45. a) 8 had seen exactly one b) 6 had only seen SW

This page titled 14.4: Sets is shared under a CC BY-SA 3.0 license and was authored, remixed, and/or curated by David Lippman (The OpenTextBookStore) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.