Salam. Is it permissible for a child who is 11 years old to show a book that has a cover of an unveiled woman that they like/love this book online?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

It appears to us –Allah knows best –that if this book includes a useful content that is not found in other books, then there is no harm in benefitting from it and presenting it to the public even with the existence of this picture.

The presence of such images in some books, especially the scientific ones, is something which has become widespread and it is very difficult to avoid. Forbidding them in this case would make things difficult for the nation.

In addition to this, (when buying the book) these images are not the intention behind buying (or reading) them, and it is not possible to avoid them.

Indeed hardship entails easiness, as in the famous jurisprudence rule.

Shaykh Ibn 'Uthaymeen distinguished between magazines and newspapers that were prepared for photography (to display pictures), and magazines that were not prepared for photography, but they include pictures in them. He stated that the first type is forbidden to buy, sell, and keep; whereas the second type is not.

It should be noted that this child at this age has most likely not reached the age of puberty, so there is no sin on him in at all. Indeed, in the event of forbidden matters, the guardian is not allowed to enable him to do that or get exposed to them, as stated by the scholars.

Allah knows best.