Exercise 3.2.1

3, namely ${\displaystyle a,b}$ and ${\displaystyle \{a,b\}}$

1. False

2. True

3. True

4. False

5. False

6. False

7. False

8. True

9. True

Exercise 3.2.3

1

The set of even integers

3

The set of all rational numbers.

Exercise 3.2.4

1

The set of all fathers

2

The set of all grandparents

3

The set of all people that are married to a woman

4

The set of all siblings

5

The set of all people that are younger than someone

6

The set of all people that are older than their father

Exercise 3.2.5

1

${\displaystyle \{x\in R|x>0\}}$

2

${\displaystyle \{x\in Z|}$ there exist ${\displaystyle y\in Z}$ such that ${\displaystyle x=2*y+1\}}$

3

${\displaystyle \{x\in R|}$ there exist ${\displaystyle y\in N}$ such that ${\displaystyle 5*y*x=1\}}$

5

${\displaystyle \{x\in N|}$ there exist ${\displaystyle y\in N}$ such that ${\displaystyle x=4*y+1\}}$

Exercise 3.2.8

ethan de bloach where are you boss ,please provide a solution manual for your book

Exercise 3.2.9

A = {1,2}, B = {1,{1,2}}

Exercise 3.2.10

Using the definition of a subset: For any xA, then xB, and because xB, xC. The same goes for any yB or any zC.

Exercise 3.2.13

${\displaystyle {\mathcal {P}}(A)=\{\emptyset ,x,y,z,w,\{x,y\},\{x,z\},\{x,w\},\{y,z\},\{y,w\},\{z,w\},\{x,y,z\},\{x,y,w\},\{x,z,w\},\{y,z,w\},\{x,y,z,w\}\}}$

Exercise 3.2.14

Bhotne kay khud kuch nahe karna bas sara is website se dekh kar chapna.

Exercise 3.2.15

1

${\displaystyle {\mathcal {P}}({\mathcal {P}}(\emptyset )=\{\emptyset ,\{\emptyset \}\}}$

2

[itex]\mathcal P( \mathcal P ( \{ \emptyset \} ) = \{ \emptyset, \{ \emptyset \}, \{ \{ \