Question

lf A= {3, 5, 7, 9, 11}, B={7, 9, 11, 13 }, C={11, 13, 15} and D={15, 17 }; find $(A \cup D) \cup (B \cup C)$

Answer 1

we know, if two sets A and B are given then, intersection of A and B is the set of all distinct elements that are in both A and B. it is denoted by $A\cap B$ or $B\cap A$. in figure, shaded region indicates $A\cap B$.
and A union B is the set of all distinct elements that are in Both A or B. it is denoted by $A\cup B$. in 2nd figure, it is clearly shown.

here, A= {3, 5, 7, 9, 11}, B={7, 9, 11, 13 }, C={11, 13, 15} and D={15, 17 }.

A U D = {3, 5, 7, 9, 11} U {15, 17} = {3, 5, 7, 9, 11, 15, 17}
B U C = {7, 9, 11, 13} U {11, 13, 15} = {7, 9, 11, 13, 15}

so, $(A\cup D)\cap(B\cup C)$ = {3, 5, 7 9, 11, 15} $\cap$ { 7, 9, 11, 13, 15}
= { 7, 9, 11, 15}

[ note : in question , there is little mistake here they should ask $(A\cup D)\cap (B\cup C)$ by mistake they ask $(A\cup D)\cup(B\cup C)$ ]