Question

A.     List all the subsets of the following sets.

2. {1,2,Ø}

8. {{0,1},{0,1,{2}},{0}}

B. Write out the following sets by listing their elements between braces.

12. {X:X ⊆{3,2,a} and │X│=1

C. Decide if the following statement is tru or false. Explain.

14. R²⊆R³

Answer 1

A.     Let us list all the subsets of the following sets.

2. The subsets of the set $\{1,2,\emptyset\}$ are $\emptyset, \{0\},\{1\},\{\emptyset\},\{1,2\},\{1,\emptyset\},\{2,\emptyset\}, \{1,2,\emptyset\}.$

8. The subsets of the set $\{\{0,1\},\{0,1,\{2\}\},\{0\}\}$ are $\emptyset, \ \{\{0,1\}\},\ \ \{\{0,1,\{2\}\}\},\ \{\{0\}\}, \ \{\{0,1\},\{0,1,\{2\}\}\},\newline \{\{0,1\},\{0\}\},\ \{\{0,1,\{2\}\},\{0\}\}, \ \{\{0,1\},\{0,1,\{2\}\},\{0\}\}.$

B. Let us write out the following sets by listing their elements between braces.

12. $\{X:X \subset \{3,2,a\}\text{ and }│X│=1\}=\{\{3\},\{2\},\{a\}\}.$

C. Let us decide if the following statement is true or false.

14. The statement $\mathbb R^2⊆ \mathbb R^3$ is false because the elements of $\mathbb R^2$ are pairs $(x,y)$ of real numbers $x$ and $y$, but the the elements of $\mathbb R^3$ are triples $(x,y,z)$ of real numbers $x,y$ and $z.$