Property 5
Difference of Two Sets
\(A\setminus B=\{x\mid x\in A\text{ and }x\notin B\}\)
1.
\(A=\{a,b,c\}\)
\(B=\{a,2,3\}\)
\(\Rightarrow A\setminus B=?\)
2.
\(A=\{1,2,a,b\}\)
\(B=\{\{1,2\},a\}\)
\(\Rightarrow A\setminus B=?\)
3.
\(A=\{a,\{b\},c,d\}\)
\(B=\{a,b,\{c\},d,e\}\)
\(\Rightarrow A\setminus B=?\)
4.
\(A=\{x\mid x\in\mathbb{N}\quad-1<x<6\}\)
\(B=\{y\mid y\in\mathbb{N}\quad0<y<3\}\)
\(\Rightarrow A\setminus B=?\)
5.
\(A=\{x\mid x\in\mathbb{N}\quad-3\le x<5\}\)
\(B=\{y\mid y\in\mathbb{N}\quad-1<y<4\}\)
\(\Rightarrow n(A\setminus B)=?\)
6.
\(A=\{x\mid x\in\mathbb{Z}\quad-2<x<6\}\)
\(B=\{y\mid y\in\mathbb{R}\quad-1<x\le5\}\)
\(\Rightarrow A\setminus B=?\)
7.
\(A=\{x\mid x\in\mathbb{Z}\quad|x|<2\}\)
\(B=\{y\mid y\in\mathbb{Z}\quad|y-1|<2\}\)
\(\Rightarrow n(A\setminus B)=?\)
8.
\(A=\{x\mid x\in\mathbb{Z}\quad|x|\le3\}\)
\(B=\{y\mid y\in\mathbb{Z}\quad|y|>-2\}\)
\(\Rightarrow A\setminus B=?\)
Property 6
Complement of a Set
\(A'=\{x\mid x\notin A\text{ and }x\in U\}\)
- \(\varnothing'=U\)
- \(U'=\varnothing\)
- \((A')'=A\)
- \(A'=U\setminus A\)
- \(A\cup A'=U\)
- \(A\cap A'=\varnothing\)
1.
\(U=\{1,2,3,4,5,6\}\)
\(A=\{1,2\}\)
\(\Rightarrow A'=?\)
2.
\(A\subset U\quad B\subset U\)
\(n(U)=14\)
\(n(A)=8\)
\(n(A\cap B)=2\)
\(n(A\cup B)=12\)
\(\Rightarrow n(B')=?\)
3.
\(A\subset U\quad B\subset U\)
\(n(B')=6\)
\(n(A'\cap B')=2\)
\(\Rightarrow n(A\setminus B)=?\)
4.
\(A\subset U\quad B\subset U\)
\(n(A\cap B')=3\)
\(n(B\cap A')=4\)
\(n(A\cap B)=2\)
\(n((A\cup B)')=3\)
\(\Rightarrow n(U)=?\)
5.
\(A\subset U\quad B\subset U\)
\(n(A)+n(B)=12\)
\(n(A')+n(B')=16\)
\(\Rightarrow n(U)=?\)
6.
\(A\subset U\quad B\subset U\)
\(n(A\cap B')=4\)
\(n(B)=8\)
\(n(A'\cap B')=4\)
\(\Rightarrow n(U)=?\)