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

Explanation:

Step1: Recall the definition of union

The union of two sets \(A\) and \(B\), denoted as \(A\cup B\), is the set of all elements that are in \(A\) or in \(B\) (or in both).

Step2: Analyze each region

• Region I: Elements only in \(A\).
• Region II: Elements in both \(A\) and \(B\).
• Region III: Elements only in \(B\).
• Region IV: Elements neither in \(A\) nor in \(B\).

Since \(A\cup B\) includes elements in \(A\) or \(B\) (or both), it includes Region I (only \(A\)), Region II (both \(A\) and \(B\)), and Region III (only \(B\)).

Answer:

I, II, and III