Property 1
Notations
\(A=\{1,2,3,a,b,\{3\},\{4,5\}\}\)
| \(1\in A\) | Correct | \(\{1\}\in A\) | Wrong |
| \(3\in A\) | Correct | \(\{3\}\in A\) | Correct |
| \(2\subset A\) | Wrong | \(\{2\}\subset A\) | Correct |
| \(\{4,5\}\in A\) | Correct | \(\{\{4,5\}\}\subset A\) | Correct |
Which of the following notations are correct?
1.
\(A=\{1,2,\{a\},\{b,c\}\}\)
\(\mathrm{I)}\ 2\in A\)
\(\mathrm{II)}\ a\in A\)
\(\mathrm{III)}\ \{b,c\}\in A\)
2.
\(A=\{1,4,9,\{3,1\},\{1\}\}\)
\(\mathrm{I)}\ 7\notin A\)
\(\mathrm{II)}\ \{3,1\}\subset A\)
\(\mathrm{III)}\ \{1\}\subset A\)
3.
\(A=\{3,4,5,\{1,2\}\}\)
\(\mathrm{I)}\ 3\subset A\)
\(\mathrm{II)}\ \{4,5\}\subset A\)
\(\mathrm{III)}\ \{1,2\}\in A\)
4.
\(A=\{\{a,b\},2,4,c\}\)
\(\mathrm{I)}\ \{a,b\}\subset A\)
\(\mathrm{II)}\ \{2\}\notin A\)
\(\mathrm{III)}\ \{4,c\}\in A\)
5.
\(A=\{b,e,\{1,3\},4\}\)
\(\mathrm{I)}\ b\subset A\)
\(\mathrm{II)}\ b\in A\)
\(\mathrm{III)}\ \{\{1,3\}\}\subset A\)
6.
\(A=\{1,2,3\}\)
\(\mathrm{I)}\ \{1\}\subset A\)
\(\mathrm{II)}\ \{1,2\}\subset A\)
\(\mathrm{III)}\ \{1,2,3\}\in A\)
Property 2
The number of elements of set A is denoted by n(A). In list form, the elements inside the \(\{\}\) notation are considered as one.
\(A=\{1,2,\{3,4\},\{5,6,7\}\}\Rightarrow n(A)=4\)
1.
\(A=\{1,3,\{a,b\}\}\)
\(\Rightarrow n(A)=?\)
2.
\(A=\{2,3,\{1,5,6\},-3,4\}\)
\(\Rightarrow n(A)=?\)
3.
\(A=\{1,2,\{0,b\},\{c,d,e\}\}\)
\(\Rightarrow n(A)=?\)
4.
\(A=\{x\mid x\in\mathbb{N},\ -4<x<6\}\)
\(\Rightarrow n(A)=?\)
5.
\(A=\{x\mid x\in\mathbb{Z},\ x^2<30\}\)
\(\Rightarrow n(A)=?\)
6.
\(A=\{x\mid7<x<13,\ x\in\mathbb{Z}\}\)
\(\Rightarrow n(A)=?\)
7.
\(A=\{x\mid x=3k,\ k\in\mathbb{Z},\ 0<x<70\}\)
\(\Rightarrow n(A)=?\)