Relations, Functions and Cartesian Product

Practice Questions

Set Theory › Relations, Functions and Cartesian Product

Questions

10

1

For a bijective function from set to set defined by $f:A \rightarrow B$ , which of the following does NOT need to be true?

2

Determine if the following statement is true or false:

If be the set defined as,

$A=\begin{Bmatrix} x,\begin{Bmatrix} x,y,z \end{Bmatrix}, \begin{Bmatrix} y,z \end{Bmatrix} \end{Bmatrix}$

then

$x\subseteq A$ .

3

For an injective function from set to set defined by $f:A \rightarrow B$ , which of the following does NOT need to be true?

4

Determine if the following statement is true or false:

If be the set defined as,

$A=\begin{Bmatrix} x,\begin{Bmatrix} x,y,z \end{Bmatrix}, \begin{Bmatrix} x,z \end{Bmatrix} \end{Bmatrix}$

then $x\subseteq A$ .

5

For a surjective function from set to set defined by $f:A \rightarrow B$ , which of the following does NOT need to be true?

6

Determine if the following statement is true or false:

If $D\subseteq E$ and $F\subseteq G$ then $D\times F\subseteq E\times G$ .

7

For which of the following pairs is the cardinality of the two sets equal?

8

What type of function is $f:\mathbb{Z}\rightarrow \mathbb{N}$ where $x \mapsto \left |x \right |$ ?

9

What type of function is $f:\mathbb{N}\rightarrow \mathbb{Z}$ where $x \mapsto x^2$ ?

10

What type of function is $f:\mathbb{Z}\rightarrow \mathbb{R}$ where $x \mapsto \sqrt{x}$ ?

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