Sylogistically logical

Logic Level 3

Let $\text{A} = \{1,2,3,4\}$ and $\text{R} = \{(1,1),(2,2),(3,3),(4,4),(1,2),(4,3),(3,2),(2,1),(3,4)\}$ be a relation on $\text{A}$ . Then is $\text{R}$ transitive?

No Insufficient information Yes

1 solution

Ashish Menon
Jul 5, 2016

In the set $\text{R}$ according to $(3,2)$ $3$ is related to $2$ , according to $(4,3)$ , $4$ is related to $3$ , but it should contain $(4,2)$ meaning that $4$ is related to $2$ which is absent in the set. Thus $\text{R}$ is $\color{#3D99F6}{\boxed{\text{not}}}$ transitive.

Your example shows that $R$ is not symmetric, but does not address the matter of transitivity. To this end, we note that with $(4,3)$ and $(3,2)$ being elements of $R$ we would require that $(4,2)$ also be an element of $R$ for it to be transitive, which is not the case, thus proving that $R$ is not transitive.

Brian Charlesworth - 4 years, 11 months ago

Thanks! I changed it! :)

Ashish Menon - 4 years, 11 months ago

I answered insufficient information. I feel it is the same as saying the solution does not indicate that our relation is not transitive. There is a misleading answer in your answer.

Hana Wehbi - 4 years, 11 months ago

Sylogistically logical

1 solution

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