Question

use the following venn diagram to find $(a \cup b)^c$. venn diagram: set a (purple) contains a, b, c; intersection of a and b contains d, e; set b (green) contains f, g, h, i; universal set (rectangle) outside a and b contains j, k, l, m. multiple - choice options: \\{c,e,k\\}, \\{a,h,p\\}, \\{t,u,v\\}, \\{j,k,l,m\\}, \\{d,l,y\\}, $\emptyset$

Explanation:

Step1: Find \( A \cup B \)

The union of sets \( A \) and \( B \) (\( A \cup B \)) includes all elements in \( A \), in \( B \), or in both. From the Venn diagram, set \( A \) has elements \( \{a, b, c, d, e\} \) and set \( B \) has elements \( \{d, e, f, g, h, i\} \). So \( A \cup B=\{a, b, c, d, e, f, g, h, i\} \).

Step2: Find the complement of \( A \cup B \)

The complement of \( A \cup B \) (\( (A \cup B)^c \)) includes all elements in the universal set (the rectangle) that are not in \( A \cup B \). The universal set here has elements outside \( A \) and \( B \), which are \( \{j, k, l, m\} \).

Answer:

\(\{j, k, l, m\}\) (corresponding to the option \([j,k,l,m]\))