Question

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

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 $A\cap(B\cup D)$
first of all , we have to find $B\cup D$
so, $B\cup D$ = {7, 9, 11, 13} $\cup$ {15, 17}
= {7, 9, 11, 13, 15, 17}
now, $A\cap(B\cup D)$ = {3, 5, 7, 9, 11} $\cap$ {7, 9, 11, 13, 15, 17}
= {7, 9, 11}