# A preference relation $\succ$ is defined as $(x_1,y_1)\succ (x_2,y_2)$ if $x_1>x_2$ and $y_1> y_2$

Does this satisfy completeness property? I need an intuitive explanation of this preference relation as well.

I am confused about the way how this relation is defined. The commodity Y in the first bundle is strictly preferred to the commodity Y in second bundle.

• What's the definition of the completeness property? Perhaps that could be a good start. – Art Sep 26 '19 at 17:05
• What happens if you compare $(1,6)$ against $(2,3)$, and $(1,6)$ against $(4,5)$, and $(2,3)$ against $(4,5)$? – Henry Sep 26 '19 at 18:13

Completeness property says that for any $$a,b\in R$$ with $$a=(x_1,y_1)$$ and $$b=(x_2,y_2)$$ , $$\:$$ $$a\succ b$$ or $$b\succ a$$ or both must be satisfied. However for any $$x_1\le x_2$$ and $$y_2\le y_1$$ neither $$a\succ b$$ nor $$b\succ a$$ , thus the completeness property doesn't satisfied.