Question

use the following venn diagram to find ( a cup b ). venn diagram: circle a (purple) contains a, b, c; overlap with circle b (green) contains d, e; circle b contains f, g, h, i; outside both circles (universal set) contains j, k, l, m. multiple - choice options: ({a,b,d,e,f,i,j,p,q}), ({a,e,g,k,r,t,x,y,z}), ({a,d,h,j,q,s,t,v,y}), ({a,b,c,d,e,f,g,h,i}), ({c,d,g,i,l,o,q,v,y}), (emptyset)

Explanation:

Step1: Recall the definition of union

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

Step2: Identify elements in set \( A \)

From the Venn diagram, set \( A \) (purple circle) contains elements: \( a, b, c, d, e \).

Step3: Identify elements in set \( B \)

From the Venn diagram, set \( B \) (green circle) contains elements: \( d, e, f, g, h, i \).

Step4: Combine elements for \( A \cup B \)

Combine all unique elements from \( A \) and \( B \). So we take \( a, b, c \) from \( A \), \( f, g, h, i \) from \( B \), and \( d, e \) (which are in both) once. This gives \( \{a, b, c, d, e, f, g, h, i\} \).

Answer:

\(\{a, b, c, d, e, f, g, h, i\}\) (corresponding to the option \(\{a,b,c,d,e,f,g,h,i\}\))