Help with a Relation

**minkyboodle** · October 12th 2009, 03:58 PM

Consider the relation R on {1,2,3,4,5} given by xRy $\longleftrightarrow$ x + y >5

How do I make the matrix for this relation?

Is the relation transitive? Why?

**Defunkt** · October 13th 2009, 02:00 AM

Originally Posted by minkyboodle

Consider the relation R on {1,2,3,4,5} given by xRy $\longleftrightarrow$ x + y >5

How do I make the matrix for this relation?

Is the relation transitive? Why?

I suppose the matrix for the relation would be defined as:

$A = (a_{ij}); \ a_{ij} = \begin{cases} 1 & i+j \geq 5 \\ 0 & i+j < 5 \end{cases}$

The relation is transitive if for any $x,y,z \in \{1,2,3,4,5\} : x+y \geq 5 , y+z \geq 5 \Rightarrow x+z \geq 5$

But what happens if you take $x=1, y=5, z=2$ ? Is $x+z \geq 5$ ?

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