Axiomatic Set Theory

Practice Questions

Set Theory › Axiomatic Set Theory

Questions

Let denote all parabolas in the Cartesian plane. Does , , or both belong to ?

$\S\begin{Bmatrix} (x,y): y=2x^2\end{Bmatrix} \T\begin{Bmatrix} (x,y):y=-x+1 \end{Bmatrix}$

Let denote all straight lines in the Cartesian plane. Does , , or both belong to ?

$\S\begin{Bmatrix} (x,y): y=2x+7 \end{Bmatrix} \T\begin{Bmatrix} 2,4,6,9 \end{Bmatrix}$

Determine if the following statement is true or false:

In accordance with primitive concepts and notations in set theory, many axioms are deducible from other axioms.

Determine if the following statement is true or false:

In accordance to primitive concepts and notations in set theory, many axioms lead to paradoxes.

Which of the following describes the relationship between the inhabited sets and if $X \cap Y = \varnothing$ ?

Which of the following represents $\left ( A\cup B\right )\cap C$ , where $A=\left { 1,2,5\right }$ , $B=\left { 3,8,10\right }$ , and $C=\left { 2n|n\in \mathbb{N}\right }$ ?

Which of the following represents $\left ( A\cap B\right )\cup C$ , where $A=\left { 1,2,5\right }$ , $B=\left { 3,8,10\right }$ , and $C=\left { 2,4,6,8\right }$ ?

For two sets, and , which of the following correctly expresses $\left | A\right | + \left | B\right |$ ?

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