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Does anyone know how to make this table? I can do a table with normal values but the $x^2$ throws me off.

'Write the relation as a table, the relation $\mathbb{Z}$ on $\{1,2,3,4\}$ by $(x,y) \in \mathbb{Z}$ if $x^2\geq y$.'

Thanks!

Tim Ratigan
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tony
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1 Answers1

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$$\begin{matrix} xRy & 1 & 2 & 3 & 4 \\ 1 & T & F & F & F \\ 2 & T & T & T & T \\ 3 & T & T & T & T \\ 4 & T & T & T & T \end{matrix}$$

You simply need to evaluate the truth value of each relation. $2R1\iff 2^2\geq1$, so $2R1$ is true. Comment if you have questions, there's nothing complicated about this.

Tim Ratigan
  • 7,247
  • This is a truth table, the text example is asking for a relation as a table, with the prior example having the table listing coordinate pairs. So I'm not sure if what you have is what its asking for, or a table of coordinates? "Write the relation as a table" is all it says. – tony Nov 09 '13 at 23:09
  • The truth table is equivalent, as $x$ is related to $y$ whenever $xRy$ is true. If you wanted, you could rewrite the table as follows, which may be closer to what you're looking for:

    $$\begin{matrix} (1,1) & & & \ (2,1) & (2,2) & (2,3) & (2,4) \ (3,1) & (3,2) & (3,3) & (3,4) \ (4,1) & (4,2) & (4,3) & (4,4) \ \end{matrix}$$

     – Tim Ratigan Nov 09 '13 at 23:25
  • ty this makes sense now much appreciated! – tony Nov 10 '13 at 04:25