2 circles labeled Set A and Set B overlap. Set A contains 1, set B contains 3, and the overlap of the 2 circles contains 2. The number 4 is outside of the circles.

Question

2 circles labeled Set A and Set B overlap. Set A contains 1, set B contains 3, and the overlap of the 2 circles contains 2. The number 4 is outside of the circles.
If k ∈ A ∩ B, which is the most specific location of k on the Venn diagram?

I
II
III
IV

GPT-4o mini · Answer

To understand the positions in a Venn diagram involving two sets, we can label the sections of the Venn diagram as follows:

Section I (Only in Set A): Elements that are exclusive to Set A but not in Set B.
Section II (Overlap - A ∩ B): Elements that are in both Set A and Set B.
Section III (Only in Set B): Elements that are exclusive to Set B but not in Set A.
Section IV (Outside of both sets): Elements that are not in either Set A or Set B.

In the scenario you provided:

Set A contains 1 (and possibly 2),
Set B contains 3 (and possibly 2),
The overlap (A ∩ B) contains 2,
The number 4 is outside of both circles.

Given that \( k \in A \cap B \), the most specific location of \( k \) on the Venn diagram is in Section II, which represents the overlap between Set A and Set B.

Thus, the answer is II.