GSATE problem 63

Hanmanchu: I'm really enjoying this book too, but struggling with some problems throughout the book.

That's why I have checking the correct answers with help of AI (ZBaduk / Katago).

The question (problem 63) is: How can Black seal off the upper side in sente?  

The answer is straightforward, threatening to make a false eye:  

However, White can push once like this, giving him a two point better result.  

If Black fights back, the outcome depends entirely on the situation on the left, i. e. whether Black can connect or make a second eye there. Next,a or b to protect the eye.