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Flashcards: Axiomatic Set Theory

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

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

$A\subseteq T$

$\text{Neither belong to A}$

$S,T \subseteq A$

$S\subseteq A$

$T\subseteq A$

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Flashcards: Axiomatic Set Theory

Home Embed

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

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

Your answer:

$A\subseteq T$

Your answer:

$\text{Neither belong to A}$

Your answer:

$S,T \subseteq A$

Your answer:

$T\subseteq A$

Correct answer:

$S\subseteq A$

Explanation:

is a set that contains all straight lines that live in the Cartesian plane, this is a vast set. To determine if , , or both belong to , identify if the elements of each set create a straight line, and if so, then that set will be a subset of . In other words, the set will belong to .

Identify the elements in first.

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

This statement reads, contains the (x,y) coordinate pairs that live on the line y=2x+7 .

Since

y=2x+7 is a straight line that lives in the Cartesian plane, that means belongs to .

Now identify the elements in .

$T\begin{Bmatrix} 2,4,6,9 \end{Bmatrix}$

This means that the elements of are 2, 4, 6, and 9. These are four, individual, values that belong to $\mathbb{N}$ . They do not create a line in the Cartesian plan and thus does not belong to .

Therefore, answering the question, belongs to .

$S\subseteq A$

Flashcards: Axiomatic Set Theory

Home Embed

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

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

$T\subseteq A$

$\text{Neither belong to A}$

$S\subseteq A$

$S,T \subseteq A$

$A\subseteq T$

Report an Error Copyright Notice

Flashcards: Axiomatic Set Theory

Home Embed

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

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

Your answer:

$T\subseteq A$

Your answer:

$\text{Neither belong to A}$

Your answer:

$S,T \subseteq A$

Your answer:

$A\subseteq T$

Correct answer:

$S\subseteq A$

Explanation:

is a set that contains all parabolas that live in the Cartesian plane, this is a vast set. To determine if , , or both belong to , identify if the elements of each set create a straight line, and if so, then that set will be a subset of . In other words, the set will belong to .

Identify the elements in first.

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

This statement reads, contains the (x,y) coordinate pairs that live on the parabola y=2x^2 .

Since

y=2x^2 is a parabola that lives in the Cartesian plane, that means belongs to .

Now identify the elements in .

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

This means that the elements of are those that live on the straight line y=-x+1 . Thus does not create a parabola in the Cartesian plan therefore does not belong to .

Therefore, answering the question, belongs to .

$S\subseteq A$

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Flashcards: Axiomatic Set Theory

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Flashcards: Axiomatic Set Theory

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Flashcards: Axiomatic Set Theory

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Flashcards: Axiomatic Set Theory

Flashcards: Axiomatic Set Theory

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DMCA Complaint

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