I am discussing with a friend the following question:
If the language $A$ is decidable and the language $B$ is recognizable, Then the language $A \cap B$ is recognizable?
I believe it is. My point is that if the machine that recognizes B never halt in some string, so the bigger machine will never know what to answer.
The image makes my point.
But my friend says that the $A \ cap B$ is a subset of $A$, then it is decidable.