It seems you've uploaded an image with set theory and logic problems related to Venn diagrams. You specifically mentioned the task of proving the identity involving sets, starting with "A". I can see the following expression in the image:

$A \cap \overline{B} \cup B = \overline{A} \cup B$

This looks like a set theory identity that needs to be proven. Let's break it down:

Identity:

$A \cap \overline{B} \cup B = \overline{A} \cup B$

Proof:

1. Left-hand side (LHS): [ A \cap