Can we construct two sets E and F meeting the following criteria

1. $dim_H(E) = dim_H(F) = dim_H(E ∩ F)$

2. $dim_P(E), dim_P(F)$, and $dim_P(E ∩ F)$ are distinct?

Here $dim_H$ denotes the Hausdorff dimension and $dim_P$ denotes the packing dimension.

Can we construct two sets $E$ and $F$ meeting the following criteria

1. $\dim_H(E) = \dim_H(F) = \dim_H(E ∩ F)$

2. $\dim_P(E), \dim_P(F)$, and $\dim_P(E ∩ F)$ are distinct?

Here $\dim_H$ denotes the Hausdorff dimension and $\dim_P$ denotes the packing dimension.