Puzzle Booklet - F and U Compatability

These booklets are produced in Hungary by hand in limited editions; their contents are made of laser cut wood.

Two shapes are called compatible if there exists a figure that can be created using either some pieces only of the first shape or some pieces only of the second shape.  Can you show that F and U pentominoes are compatible? 

Other challenges include:
1) Create the same shape using 2F plus 1U and 1F plus 2U.
2) Create the same shape using 3F plus 1U and 1F plus 3U.
3) Create the same shape using 7F and 7U!
4) Put back the pieces into the booklet such that there is a symmetrical arrangement of holes.

Cleverly designed with an attractively innovative book cover.  Solutions are included.

Made and designed by Péter Gál.