# VC dimension and binary operations

There are two classes of binary functions, $F_1,F_2$. The VC-dimension of $F_i$ is $d_i$. Is there any simple formula for the VC-dimension of the following classes?

• $F_\lor := \{ f_1(x) \lor f_2(x) | f_1\in F_1 \text{ and } f_2\in F_2\}$
• $F_\land := \{ f_1(x) \land f_2(x) | f_1\in F_1 \text{ and } f_2\in F_2\}$