I am studying concept learning, and I am focusing on the concept of consistency for an hypotesis.
Consider an Hypotesis $h$, I have understood that it is consistent with a training set $D$ iff $h(x)=c(x)$ where $c(x)$ is the concept and this has to be verified for every sample $x$ in $D$.
For example consider the following training set:
and the following hypotesis:
I have that this is not consistent with D because for the example $3$ in $D$ we have $h(x)!=c(x)$.
I don't understand why this hypotesis is not consistent.
Infact, consider the following hypotesis:
this is consistent with $D$ because for each example in $D$ we have $h(x)=c(x)$.
But why the first hypotesis $h_1$ is not consistent while the second,$h$, is consistent?
Can somebody please explain this to me?