(𝐴 ∪ ∅) ∩ ∅ = 𝐴 where 𝐴 is a set

The statement is incorrect. Here's why:

Step 1: Understand the symbols The symbols used are from set theory. "∪" stands for union, "∩" stands for intersection, and "∅" stands for the empty set.

Step 2: Break down the equation The equation can be broken down into two parts: (𝐴 ∪ ∅) and (∅ ∩ ∅).

Step 3: Solve each part The union of any set 𝐴 and the empty set ∅ is 𝐴 itself because there are no additional elements in ∅ to add to 𝐴. So, (𝐴 ∪ ∅) = 𝐴.

The intersection of the empty set with itself is still the empty set because there are no elements in ∅ to intersect. So, (∅ ∩ ∅) = ∅.

Step 4: Combine the parts Now, we combine the two parts using the intersection operation. The intersection of set 𝐴 and the empty set ∅ is ∅ because there are no common elements between 𝐴 and ∅. So, (𝐴 ∪ ∅) ∩ ∅ = ∅.

Therefore, (𝐴 ∪ ∅) ∩ ∅ ≠ 𝐴. The statement is false.