
If \[A=\left\{ 3,6,12,15,18,21 \right\}\], \[B=\left\{ 4,8,12,16,20 \right\}\], \[C=\left\{ 2,4,6,8,10,12,14,16 \right\}\] and \[D=\left\{ 5,10,15,20 \right\}\], then find:
(i) A-D
(ii) B-A
Answer
511.8k+ views
Hint: We know that the difference of any two sets say A and B i.e. (A-B) is a set which contains all the elements of A which are not present in set B. Using this concept, we can find the sets A-D and B-A.
Complete step-by-step answer:
We have been given sets as follows:
\[A=\left\{ 3,6,12,15,18,21 \right\}\]
\[B=\left\{ 4,8,12,16,20 \right\}\]
\[C=\left\{ 2,4,6,8,10,12,14,16 \right\}\]
\[D=\left\{ 5,10,15,20 \right\}\]
Now we know that the difference between any two sets A and B i.e. (A-B) is a set that contains all the elements of A which are not present in set B.
(i) A-D
\[\Rightarrow A-D=\left\{ 3,6,12,15,18,21 \right\}-\left\{ 5,10,15,20 \right\}\]
Since the element ’15’ of A is also present in set D. So we will exclude it to get (A-D).
\[\Rightarrow A-D=\left\{ 3,6,12,18,21 \right\}\]
(ii) B-A
\[\Rightarrow B-A=\left\{ 4,8,12,16,20 \right\}-\left\{ 3,6,12,15,18,21 \right\}\]
Since the element 12 of B is also present in the set A. So we will exclude it to get (B-A).
\[\Rightarrow B-A=\left\{ 4,8,16,20 \right\}\]
Therefore, we get,
(i) \[A-D=\left\{ 3,6,12,18,21 \right\}\]
(ii) \[B-A=\left\{ 4,8,16,20 \right\}\]
Note: Be careful while finding the difference of two sets and check that in (A-D) the sets only contain the elements of A which are not present in set D and similarly of (B-A) also. Also, remember that a set is a well-defined collection of distinct objects so make sure that our sets don’t contain any repetitive elements.
Complete step-by-step answer:
We have been given sets as follows:
\[A=\left\{ 3,6,12,15,18,21 \right\}\]
\[B=\left\{ 4,8,12,16,20 \right\}\]
\[C=\left\{ 2,4,6,8,10,12,14,16 \right\}\]
\[D=\left\{ 5,10,15,20 \right\}\]
Now we know that the difference between any two sets A and B i.e. (A-B) is a set that contains all the elements of A which are not present in set B.
(i) A-D
\[\Rightarrow A-D=\left\{ 3,6,12,15,18,21 \right\}-\left\{ 5,10,15,20 \right\}\]
Since the element ’15’ of A is also present in set D. So we will exclude it to get (A-D).
\[\Rightarrow A-D=\left\{ 3,6,12,18,21 \right\}\]
(ii) B-A
\[\Rightarrow B-A=\left\{ 4,8,12,16,20 \right\}-\left\{ 3,6,12,15,18,21 \right\}\]
Since the element 12 of B is also present in the set A. So we will exclude it to get (B-A).
\[\Rightarrow B-A=\left\{ 4,8,16,20 \right\}\]
Therefore, we get,
(i) \[A-D=\left\{ 3,6,12,18,21 \right\}\]
(ii) \[B-A=\left\{ 4,8,16,20 \right\}\]
Note: Be careful while finding the difference of two sets and check that in (A-D) the sets only contain the elements of A which are not present in set D and similarly of (B-A) also. Also, remember that a set is a well-defined collection of distinct objects so make sure that our sets don’t contain any repetitive elements.
Recently Updated Pages
The correct geometry and hybridization for XeF4 are class 11 chemistry CBSE

Water softening by Clarks process uses ACalcium bicarbonate class 11 chemistry CBSE

With reference to graphite and diamond which of the class 11 chemistry CBSE

A certain household has consumed 250 units of energy class 11 physics CBSE

The lightest metal known is A beryllium B lithium C class 11 chemistry CBSE

What is the formula mass of the iodine molecule class 11 chemistry CBSE

Trending doubts
Is Cellular respiration an Oxidation or Reduction class 11 chemistry CBSE

In electron dot structure the valence shell electrons class 11 chemistry CBSE

What is the Pitti Island famous for ABird Sanctuary class 11 social science CBSE

State the laws of reflection of light

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

Difference Between Prokaryotic Cells and Eukaryotic Cells
