Question

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

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 }.
we have to find $(A\cup B)\cap(B\cup C)$
first find $A\cup B$
e.g.,A U B = {3, 5,7, 9, 11} U { 7, 9, 11, 13}
= {3, 5, 7, 9, 11, 13}
similarly, find $B\cup C$
e.g., B U C = {7, 9, 11, 13} U {11, 13, 15}
= {7, 9, 11, 13, 15}
now, $(A\cup B)\cap(B\cup C)$ = {3, 5, 7, 9, 11, 13} $\cap$ {7, 9, 11, 13, 15}
= {7, 9, 11, 13}