I bought a book for children were the pictures have a fold up flap. You can open and close the flap and it completes or breaks up the picture. Is this book mutar to be read on shabbos or is it a violation of kosev/mochek?
It is permitted to use the book on Shabbos.
The main relevant discussion of poskim pertains to assembling puzzles on Shabbos.
The Levush rules that it is forbidden to open and close a book on Shabbos that has words stamped on the edge of its pages (Levush 340:4). In his opinion, opening the book and thereby breaking the letters in this way violates a Torah prohibition of erasing; closing the book and reconstituting the letters violates writing.
Other poskim add that the Levush would also prohibit opening and closing a book where the page edges are decorated since this is considered erasing and redrawing the decoration (Machatzis HaShekel 340:6).
According to this opinion, it will not be permitted to assemble a puzzle on Shabbos.
However, other poskim do not concur with the ruling, contending that merely moving letters or parts of letters together is not considered writing, and adding that opening or closing the pages of a book is not a melacha since the book is meant to be opened and closed, just as opening or closing a door is not considered destruction and construction (Shut Rema 119; Taz 340:2).
The Levush might argue that opening and closing a door involves using the door in a normal way, wheresas opening a book with writing on its edges is not considered “normal use” of a book, because the writing and erasing that takes place on the edge of the book is incidental to opening the book. Therefore, it is seen as an act of writing and erasing on Shabbos.
Although some poskim agree with the Levush (Magen Avraham 340:6; Chazon Ish 61:1), the majority rule leniently. The Mishnah Berurah concludes that although the halacha is not like the Levush, one should preferably be stringent if one has a different book available (340:17).
For puzzles, Rav Moshe Feinstein (oral ruling, quoted in Sefer Tiltulei Shabbos, p. 25) is cited as not permitting, but Rav Shlomo Zalman Auerbach (Shemiras Shabbos K’hilchasah 16:23; Shulchan Shelomo 340:13-2) ruled that one should be stringent specifically where there is a frame for the puzzle, or where the pieces fit together tightly (see also Shalmei Yehudah, p. 90; see also Children in Halachah, p. 140, where lenient opinions are also cited).
For the question of the flaps, in this case there is no frame and no tight fitting, so that according to the ruling of the Shemiras Shabbos Kehilchasa, it will be permitted. Furthermore, the case of the flap is very similar to the case of a door that is made to open and close, in which case even the Levush will be lenient, and therefore there is certainly room to rule leniently on the matter.