Theory of Positive Integers : Sets

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Example Questions

Example Question #1 : Sets

Let 

\(\displaystyle S:\begin{Bmatrix} -10,-8,-6,-4,-2,0,2,4 \end{Bmatrix}\)

if \(\displaystyle B\) is some condition of \(\displaystyle x\) such that it can be described as \(\displaystyle \begin{Bmatrix} x\ \epsilon\ S: p(x) \end{Bmatrix}\) what is \(\displaystyle p(x)\) when \(\displaystyle B=\begin{Bmatrix} 2,4 \end{Bmatrix}\)?

Possible Answers:

\(\displaystyle B=\begin{Bmatrix} x\ \epsilon\ S: x>0 \end{Bmatrix}\)

\(\displaystyle B=\begin{Bmatrix} x\ \epsilon\ S: x\geq0 \end{Bmatrix}\)

\(\displaystyle B=\begin{Bmatrix} x\ \epsilon\ S: x\leq0 \end{Bmatrix}\)

None of the answers

\(\displaystyle B=\begin{Bmatrix} x\ \epsilon\ S: x< 0 \end{Bmatrix}\)

Correct answer:

\(\displaystyle B=\begin{Bmatrix} x\ \epsilon\ S: x>0 \end{Bmatrix}\)

Explanation:

First, identify what is given.

\(\displaystyle S:\begin{Bmatrix} -10,-8,-6,-4,-2,0,2,4 \end{Bmatrix}\)

\(\displaystyle B=\begin{Bmatrix} 2,4 \end{Bmatrix}\)

and \(\displaystyle B\) can be described in the following format

\(\displaystyle B=\begin{Bmatrix} x\ \epsilon\ S: p(x) \end{Bmatrix}\)

Since \(\displaystyle B\) contains the elements in \(\displaystyle S\) that are greater than zero, \(\displaystyle p(x)\) can be written as follows.

\(\displaystyle B=\begin{Bmatrix} x\ \epsilon\ S: x>0 \end{Bmatrix}\)

Example Question #2 : Sets

Let 

\(\displaystyle S:\begin{Bmatrix} -6,-4,-2,0,2,4 \end{Bmatrix}\)

if \(\displaystyle B\) is some condition of \(\displaystyle x\) such that it can be described as \(\displaystyle \begin{Bmatrix} x\ \epsilon\ S: p(x) \end{Bmatrix}\) what is \(\displaystyle p(x)\) when \(\displaystyle B=\begin{Bmatrix} -6,-4,-2,0 \end{Bmatrix}\)?

Possible Answers:

\(\displaystyle B=\begin{Bmatrix} x\ \epsilon\ S: x\leq0 \end{Bmatrix}\)

\(\displaystyle B=\begin{Bmatrix} x\ \epsilon\ S: x< 0 \end{Bmatrix}\)

\(\displaystyle B=\begin{Bmatrix} x\ \epsilon\ S: x>0 \end{Bmatrix}\)

\(\displaystyle B=\begin{Bmatrix} x\ \epsilon\ S: x\geq0 \end{Bmatrix}\)

None of the answers

Correct answer:

\(\displaystyle B=\begin{Bmatrix} x\ \epsilon\ S: x\leq0 \end{Bmatrix}\)

Explanation:

First, identify what is given.

\(\displaystyle S:\begin{Bmatrix} -6,-4,-2,0,2,4 \end{Bmatrix}\)

\(\displaystyle B=\begin{Bmatrix} -6,-4,-2,0 \end{Bmatrix}\)

and \(\displaystyle B\) can be described in the following format

\(\displaystyle B=\begin{Bmatrix} x\ \epsilon\ S: p(x) \end{Bmatrix}\)

Since \(\displaystyle B\) contains the elements in \(\displaystyle S\) that are less than or zero, \(\displaystyle p(x)\) can be written as follows.

\(\displaystyle B=\begin{Bmatrix} x\ \epsilon\ S: x\leq0 \end{Bmatrix}\)

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