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

On the Venn diagram, which region(s) represent the union of Set A and Set B (A⋃B)?

II
I and III
I, II, and III
I, II, III, and IV

Answer 1

In a Venn diagram, the union of two sets (A ∪ B) includes all elements that are in either set A, set B, or in both sets.

Given your description:

• Set A contains the element 1.
• Set B contains the element 3.
• The overlap contains the element 2 (which is in both sets A and B).
• The number 4 is outside of both sets.

Now, let's break down the regions in the Venn diagram:

• Region I: Represents elements that are only in Set A (which would be 1).
• Region II: Represents elements that are only in Set B (which would be 3).
• Region III: Represents elements that are in both sets A and B (which would be 2).
• Region IV: Represents elements that are outside both sets (which would be 4).

To find the union A ∪ B, we will include all elements from regions I, II, and III:

• From region I: 1 (from Set A)
• From region II: 3 (from Set B)
• From region III: 2 (common element)

Thus, the combined elements are 1, 2, and 3.

Since region IV (4) is outside the circles and is not included in A ∪ B, we do not consider it.

Therefore, the regions that represent the union of Set A and Set B (A ∪ B) are regions I, II, and III.

So the correct answer is: I, II, and III.