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I would like to know If these exercises about relations are right. I took discrete mathematics like 10 years ago, but I don't remember taking relations. I'm using a book I found online but does not have examples like these ones. I will appreciate any help.

1. Find the relation $M$ over a set $S=\{1,2,3\}$, if $M=\{(x,r(x)):r(x)=2x-1\}$

I substituted the values in the set $S$ in the equation in the set $M$.

  • For $x=1$, I got $r(x)=1$
  • For $x=2$, I got $r(x)=3$
  • For $x=3$, I got $r(x)=5$

So $M=\{(1,1),(2,3),(3,5)\}$

2. Find the set of coordinate pairs $\{(x,y)\}$ si $y=x^2-2x-3$ and $D=\{x|x\in Z, 1 \leq x\leq4\}$.

I substituted the values in the set $D$ in the equation.

  • For $x=1$, I got $y=-4$
  • For $x=2$, I got $y=-3$
  • For $x=3$, I got $y=0$
  • For $x=4$, I got $y=5$

The set of coordinate pairs is: $\{(1,-4),(2,-3),(3,0),(4,5)\}$

3. Find the relation $Q$ over $S \times T$ if $S=\{1,2,3\}$, $T=\{4,5\}$, and the correspondence rule is $r(x)=x+2$.

$S \times T = \{(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)\}$

So $Q=\{(2,4),(3,5)\}$

Thanks.

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    $\begingroup$ The terminology ‘relation $M$ over $S$’ in the first problem normally means that $M\subseteq S\times S$; since $5\notin S$, $M$ does not contain the pair $\langle 3,5\rangle$. (You handled a similar issue correctly in the third problem.) It looks fine otherwise. $\endgroup$ – Brian M. Scott Mar 26 at 2:35
  • $\begingroup$ okey. thanks so much. :) $\endgroup$ – gi2302 Mar 26 at 2:43
  • $\begingroup$ The title consists entirely of the tag names and the generic word "questions". Please consider how the main page would look if everyone chose titles like that. Broad subjects like "relations" are covered by the tags; the purpose of the title is to summarize the question more specifically. $\endgroup$ – joriki Mar 26 at 3:15

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