I am doing a past paper, and one of the question is:

Let $A = ${$cat, dog, mouse, bird$}, and let $R$ be the binary relation on $A$ given by:

$R = ${($x, y$): $x$ and $y$ have no letter in common}.

Draw $R$

I have a limited understanding of relations (after watching videos and reading books on reflexive, symmetric, transitive properties), but all the past papers I have ask me to draw a relation and I have no idea how where to start, and can not seem to find any simple resources. Please could someone guide me on this.

Edit (my attempt):

enter image description here

  • $\begingroup$ Put a labeled dot on paper for each of the four species, connect two by a line when they are related by $R$. $\endgroup$ Jan 6 '18 at 14:57
  • $\begingroup$ @EthanBolker Please see my edit in the OP, would a drawing like that be correct for the question? $\endgroup$
    – Shannon
    Jan 6 '18 at 15:33
  • $\begingroup$ obviously 'Bird' and 'Dog' don't satisfy our relation $\endgroup$
    – Yariv Levy
    Jan 6 '18 at 15:35
  • $\begingroup$ Yes, it's right now. $\endgroup$ Jan 6 '18 at 16:17

$\{ (cat, dog), (mouse, bird), (bird, cat), (cat,mouse) \}$

Every pair has no letter in common, can you see it ?

  • $\begingroup$ So would my drawing in the OP (just added it now) be correct? $\endgroup$
    – Shannon
    Jan 6 '18 at 15:35
  • $\begingroup$ It isn't, 'Bird' and 'Dog' shared -d-. $\endgroup$
    – Yariv Levy
    Jan 6 '18 at 15:36
  • $\begingroup$ Oops, my English is too bad haha. Please see updated. That drawing would be the correct answer for the question asked? $\endgroup$
    – Shannon
    Jan 6 '18 at 15:38
  • $\begingroup$ It is correct now. $\endgroup$
    – Yariv Levy
    Jan 6 '18 at 15:39
  • 1
    $\begingroup$ I'm sorry, i misunderstood you, you are right, it wouldn't connect to and other word. $\endgroup$
    – Yariv Levy
    Jan 6 '18 at 15:49

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