Test 9
1.
\(\beta=\{(1,2),(1,3),(2,2)\}\)
\(\Rightarrow \beta^{-1}=?\)
A) \(\{(2,2)\}\)B) \(\{(2,1),(3,1)\}\)C) \(\{(1,2),(1,3),(2,2)\}\)D) \(\{(1,1),(2,2),(3,3)\}\)E) \(\{(2,1),(3,1),(2,2)\}\)
2.
\(\beta=\{(x,y)\in\mathbb{Z}\times\mathbb{Z}\mid5x-2y=n\}\)
\((1,3)\in\beta^{-1}\)
\(\Rightarrow n=?\)
A) \(-1\)B) \(1\)C) \(3\)D) \(13\)E) \(14\)
3.
\(\beta=\{(x,y)\in\mathbb{Z}\times\mathbb{Z}\mid2x+3y=n\}\)
\((2,4)\in\beta^{-1}\)
\(\Rightarrow n=?\)
A) \(14\)B) \(13\)C) \(12\)D) \(11\)E) \(10\)
4.
\(A=\{1,2,3\},\quad\beta:A\to A\)
\(\beta=\{(x,y)\mid x<y,\ x,y\in A\}\)
\(\Rightarrow \beta^{-1}=?\)
A) \(\{(3,1),(3,2)\}\)B) \(\{(3,3),(3,2),(3,1)\}\)C) \(\{(3,1),(3,2),(2,1)\}\)D) \(\{(1,3),(2,3),(1,2)\}\)E) \(\{(1,1),(2,2),(3,3)\}\)
5.
\(\beta=\{(x,y)\mid2x+y=9,\quad x,y\in\mathbb{Z}^+\}\)
\(\Rightarrow \beta^{-1}=?\)
A) \(\{(1,4),(3,3),(5,2)\}\)B) \(\{(1,4),(5,2),(7,2)\}\)C) \(\{(4,1),(3,3),(5,2),(1,7)\}\)D) \(\{(1,4),(3,3),(5,2),(7,1)\}\)E) \(\{(4,1),(5,2),(7,1)\}\)
6.
\(\beta=\{(x,y)\in\mathbb{Z}\times\mathbb{Z}\mid2x+3y=24\}\)
\(\Rightarrow \beta^{-1}=?\)
A) \(\beta^{-1}=\{(y,x)\in\mathbb{Z}\times\mathbb{Z}\mid3x+2y=24\}\)B) \(\beta^{-1}=\{(x,y)\in\mathbb{Z}\times\mathbb{Z}\mid2x+3y=24\}\)C) \(\beta^{-1}=\{(y,x)\in\mathbb{Z}\times\mathbb{Z}\mid6x+y=24\}\)D) \(\beta^{-1}=\{(x,y)\in\mathbb{Z}\times\mathbb{Z}\mid3x+2y=24\}\)E) \(\beta^{-1}=\{(y,x)\in\mathbb{Z}\times\mathbb{Z}\mid x+6y=24\}\)
7.
\(\beta=\{(x,y)\in\mathbb{Z}\times\mathbb{Z}:2|x|+|y|=4\}\)
\(\Rightarrow n(\beta)=?\)
A) \(4\)B) \(6\)C) \(8\)D) \(10\)E) \(12\)
8.
\(\beta=\{(a,c),(c,d),(b,b),(b,a),(c,a),(d,a),(d,c)\}\)
\(\Rightarrow n(\beta\cap\beta^{-1})=?\)
A) \(1\)B) \(2\)C) \(3\)D) \(4\)E) \(5\)