Question

use the following venn diagram to find ( a^c ).
venn diagram: universal set (rectangle) with two circles a (purple, elements a, b, c) and b (green, elements f, g, h, i); overlap (d, e); outside both circles: j, k, l, m
options:
○ {f,g,h,i,j,k,l,m}
○ {a,b,g,j,p,r,u,y}
○ {b,d,f,k,m,w,x,y}
○ {e,h,i,k,l,r,x,y}
○ {c,f,g,i,o,p,s,v}
○ ∅

Explanation:

Step1: Recall Complement Definition

The complement of a set \( A \) (denoted \( A^c \)) consists of all elements in the universal set that are not in \( A \).

Step2: Identify Universal Set and Set \( A \)

From the Venn diagram, the universal set (the rectangle) contains elements: \( a, b, c, d, e, f, g, h, i, j, k, l, m \).
Set \( A \) (the purple circle) contains elements: \( a, b, c, d, e \).

Step3: Find Elements Not in \( A \)

Elements in the universal set but not in \( A \) are: \( f, g, h, i, j, k, l, m \).

Answer:

\(\{f, g, h, i, j, k, l, m\}\)