
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 \[{\text{A}} - ({\text{B}} \cap {\text{C}})\].
Answer
516.6k+ views
Hint:- Draw Venn’ 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 Venn’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.

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 Venn’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.
Recently Updated Pages
Glucose when reduced with HI and red Phosphorus gives class 11 chemistry CBSE

The highest possible oxidation states of Uranium and class 11 chemistry CBSE

Find the value of x if the mode of the following data class 11 maths CBSE

Which of the following can be used in the Friedel Crafts class 11 chemistry CBSE

A sphere of mass 40 kg is attracted by a second sphere class 11 physics CBSE

Statement I Reactivity of aluminium decreases when class 11 chemistry CBSE

Trending doubts
10 examples of friction in our daily life

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

Difference Between Prokaryotic Cells and Eukaryotic Cells

State and prove Bernoullis theorem class 11 physics CBSE

What organs are located on the left side of your body class 11 biology CBSE

How many valence electrons does nitrogen have class 11 chemistry CBSE
