# Find VC dimension

I'm studying theoretical machine learning at university, and I have this problem in textbook, that I have no Idea how to start. In space $$X=R^2$$ are given two models $$H_1$$ (rectangle with sides parallel to the coordinate axes) and $$H_2$$ (lines). We define a model $$H_3$$ such that every hypothesis is a combination of one hypothesis from $$H_1$$ and one from $$H_2$$. Prove or disprove that the model $$H_3$$ has a bigger VC dimension (Vapnik–Chervonenkis dimension) then the VC dimensions of the models $$H_1$$ and $$H_2$$.

I need to find VC of $$H_1$$, $$H_2$$, and combined of $$H_3$$.

• examples of VC computation here but I fail to understand the $H_1$ and $H_2$ sets, in yout question Apr 20, 2021 at 7:15
• @NikosM. so the first is rectangle with sides parallel to the coordinate axes and second are just straight lines. In textbook I found that VC (H2)=3 and VC(H1)=4 but I don't know how to get the VC dimension of H3? Apr 20, 2021 at 8:28
• If you understand how $VC(H_1)$ and $VC(H_2)$ are derived then it can help derive the combined VC Apr 20, 2021 at 15:57
• Please credit the original source of all copied material: datascience.stackexchange.com/help/referencing. The same exercise is posted here, so something has been copied from somewhere: cs.stackexchange.com/q/139171/755, datascience.stackexchange.com/q/93279/8560.
– D.W.
Apr 20, 2021 at 17:36
• @NikosM. I understand and found that VC(H1)=3 and VC(H2)=4. But how can I combine them ? Apr 20, 2021 at 20:42