Property 3
Coordinate Plane
1.
\(\Rightarrow A\setminus B=?\)
2.
\(\Rightarrow A\setminus B=?\)
3.
\(A=\{x\mid|x|\le3\quad x\in\mathbb{R}\}\)
\(B=\{y\mid1<y<4\quad y\in\mathbb{R}\}\)
\(\Rightarrow \text{Graph }(A\times B)=?\)
Property 4
Relation
Let A and B be sets.
Any subset of \(A\times B\) is called a relation from A to B and it is denoted as \(\beta:A\to B\)
\(\beta:A\to B\)
\(\beta=\{(a,1),(a,2),(b,3),(c,1)\}\)
\(\beta^{-1}=\{(x,y)\mid(x,y)\in\beta\}\)
is called inverse \(\beta\) relation.
1.
\(\beta=\{(x,y)\mid x\cdot y=6\quad x,y\in\mathbb{Z}^+\}\)
\(\Rightarrow \beta=?\)
2.
\(\beta=\{(x,y)\mid x+y=6\quad x,y\in\mathbb{N}\}\)
\(\Rightarrow n(\beta)=?\)
3.
\(A=\{1,2,3\}\)
\(\beta:A\to A\)
\(\beta:\{(x,y)\mid x\le y\quad x,y\in A\}\)
\(\Rightarrow n(\beta)=?\)
4.
\(\beta:\{(x,y)\mid3x+a=y,\quad x,y\in\mathbb{R}\}\)
\((1,7)\in\beta\)
\(\Rightarrow a=?\)
5.
\(\beta=\{(1,2),(1,3),(4,4)\}\)
\(\Rightarrow \beta^{-1}=?\)
6.
\(\beta:\{(x,y)\in\mathbb{Z}\times\mathbb{Z}\mid x+3y=k\}\)
\((1,3)\in\beta^{-1}\)
\(\Rightarrow k=?\)