Test 3
1.
\(A=\{a,b,c\}\)
\(B=\{d,e,f,g\}\)
\(C=\{a,c,d,e\}\)
\(\Rightarrow n[(A\times B)\cup(C\times B)]=?\)
A) \(8\)B) \(16\)C) \(20\)D) \(36\)E) \(48\)
2.
\(A\times B=\{(2,1),(2,2)\}\)
\(n(C)=4\)
\(\Rightarrow n[(A\times C)\cap(B\times C)]=?\)
A) \(2\)B) \(4\)C) \(6\)D) \(8\)E) \(10\)
3.
\(B\cap C=\{1,2,3,4\}\)
\(n[(B\times A)\cap(C\times A)]=20\)
\(\Rightarrow n(A)=?\)
A) \(20\)B) \(15\)C) \(10\)D) \(5\)E) \(4\)
4.
\(A\times B=\{(1,3),(1,a),(a,3),(a,a),(3,a),(3,3)\}\)
\(n(C)=5\)
\(\Rightarrow n[(A\times C)\cap(B\times C)]=?\)
A) \(5\)B) \(10\)C) \(15\)D) \(20\)E) \(25\)
5.
\(\samefrac{n(A)}{n(A\times B)}\in\mathbb{Z}\)
\(B\ne\varnothing\)
\(\Rightarrow n(B)=?\)
A) \(0\)B) \(1\)C) \(2\)D) \(3\)E) \(4\)
6.
\(A\subset B\)
\(n[(A\times B)-(A\times A)]=5\)
\(\Rightarrow n(B)=?\)
A) \(7\)B) \(6\)C) \(5\)D) \(4\)E) \(3\)
7.
\(A=\{a,b,c,d,e\}\)
\(B=\{b,c,f\}\)
\(C=\{2,3\}\)
\(\Rightarrow [(A\times C)\cap(B\times C)]^{-1}=?\)
A) \(\{(2,a),(2,e),(3,a),(3,e)\}\)B) \(\{(2,a),(2,e),(3,c),(3,d)\}\)C) \(\{(a,a),(a,c),(b,c)\}\)D) \(\{(2,b),(2,c),(3,b),(3,c)\}\)E) \(\{(2,b),(2,c),(2,f),(3,b),(3,c),(3,f)\}\)
8.
\(A=\{x\mid x\in\mathbb{Z},\quad|x-1|<3\}\)
\(n[(A\times B)\cup(A\times A)]=30\)
\(\Rightarrow n(A\cup B)=?\)
A) \(2\)B) \(3\)C) \(4\)D) \(5\)E) \(6\)