Question

on the venn diagram, which region(s) represent the union of set a and set b ($acup b$)?
○ ii
○ i and iii
○ i, ii, and iii
○ i, ii, iii, and iv

Explanation:

The union of two sets \( A \) and \( B \) (denoted \( A \cup B \)) includes all elements that are in \( A \), in \( B \), or in both. In the Venn diagram:

• Region I: Elements only in Set A.
• Region II: Elements in both Set A and Set B.
• Region III: Elements only in Set B.

So, \( A \cup B \) includes regions I, II, and III (since these are all elements in A, in B, or in both). Region IV is outside both sets, so it is not part of the union.

Answer:

I, II, and III