Question

# If ${\text{A}} = \{ 10,15,20,25,30,35,40,45,50\}$,${\text{B}} = \{ 1,5,10,15,20,30\}$ and ${\text{C}} = \{ 7,8,15,20,35,45,48\} ,$ find ${\text{A}} - ({\text{B}} \cap {\text{C}})$.

Hint:- Draw Vennâ€™ diagram. First find ${\text{B}} \cap {\text{C}}$.

As, we are given with three sets and that were,
$\Rightarrow {\text{A}} = \{ 10,15,20,25,30,35,40,45,50\} ,$
$\Rightarrow {\text{B}} = \{ 1,5,10,15,20,30\}$ and
$\Rightarrow {\text{C}} = \{ 7,8,15,20,35,45,48\}$
And asked to find ${\text{A}} - ({\text{B}} \cap {\text{C}})$.
And as we know that in set theory $\cap$ depicts intersection.
$\Rightarrow$An intersection of two sets gives us the common elements of both sets.
So, ${\text{B}} \cap {\text{C}}$ will give us common elements of sets B and C
$\Rightarrow$So, ${\text{(B}} \cap {\text{C) }} = {\text{ }}\{ 1,5,10,15,20,30\} \cap \{ 7,8,15,20,35,45,48\} = \{ 15,20\}$
As we know that if X and Y are some sets then,
$\Rightarrow$X-Y will give us a set having all elements of X excluding elements of Y.
So, ${\text{A}} - ({\text{B}} \cap {\text{C}})$ will give us those elements of set A which are not in set ${\text{(B}} \cap {\text{C)}}$
$\Rightarrow$${\text{A}} - ({\text{B}} \cap {\text{C}}) = \{ 10,15,20,25,30,35,40,45,50\} - \{ 15,20\}$
$\Rightarrow$Hence, ${\text{A}} - ({\text{B}} \cap {\text{C}}) = \{ 10,25,30,35,40,45,50\}$

Note:- Whenever we come up with this type of problem then first, we have to Draw Vennâ€™s diagram because this will give proper clarity for the problem. Then remember that for any set X and Y, X-Y will give us a set having all elements of
X excluding elements of Y.