Answer
Verified
412.5k+ views
Hint: First we will understand the meaning of complement of a set, and with the help of that we will find all the values that have been asked and there are some properties of complement that we will also use.
Complete step-by-step answer:
Let’s start our solution by what the universal set is.
Universal set: The set containing all objects or elements and of which all other sets are subsets.
Complement of a set: Complement of a set A, denoted by A’, is the set of all elements that belongs to the universal set but does not belong to set A.
Here we have U as the universal set and A, B, C as the subsets of U.
Now we get A’ as per the above definition as:
U – A
Therefore, by taking elements not present in A, we get
A’ = $\left\{ 5,6,7,8,9 \right\}$
Similarly we get the set B’ as:
U – B
Therefore, by taking elements not present in B, we get
B’ = $\left\{ 1,3,5,7,9 \right\}$
Similarly we get the set C’ as:
U – C
Therefore, by taking elements not present in C, we get
C’ = $\left\{ 2,3,7,8,9 \right\}$
Now there is one property of complement of a set,
$\left( A' \right)'=A$
Now we will use this property for solving part (d):
(B’)’ = B = $\left\{ 2,4,6,8 \right\}$
Hence we have found all the sets that have been asked.
Note: One should be careful of the fact that when we subtract two sets the common elements of the set which is being subtract is removed and the remaining elements is the final answer, hence this point must be kept in mind to avoid any mistake.
Complete step-by-step answer:
Let’s start our solution by what the universal set is.
Universal set: The set containing all objects or elements and of which all other sets are subsets.
Complement of a set: Complement of a set A, denoted by A’, is the set of all elements that belongs to the universal set but does not belong to set A.
Here we have U as the universal set and A, B, C as the subsets of U.
Now we get A’ as per the above definition as:
U – A
Therefore, by taking elements not present in A, we get
A’ = $\left\{ 5,6,7,8,9 \right\}$
Similarly we get the set B’ as:
U – B
Therefore, by taking elements not present in B, we get
B’ = $\left\{ 1,3,5,7,9 \right\}$
Similarly we get the set C’ as:
U – C
Therefore, by taking elements not present in C, we get
C’ = $\left\{ 2,3,7,8,9 \right\}$
Now there is one property of complement of a set,
$\left( A' \right)'=A$
Now we will use this property for solving part (d):
(B’)’ = B = $\left\{ 2,4,6,8 \right\}$
Hence we have found all the sets that have been asked.
Note: One should be careful of the fact that when we subtract two sets the common elements of the set which is being subtract is removed and the remaining elements is the final answer, hence this point must be kept in mind to avoid any mistake.
Recently Updated Pages
Assertion The resistivity of a semiconductor increases class 13 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE
Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE
What are the possible quantum number for the last outermost class 11 chemistry CBSE
Is C2 paramagnetic or diamagnetic class 11 chemistry CBSE
Trending doubts
State the differences between manure and fertilize class 8 biology CBSE
Why are xylem and phloem called complex tissues aBoth class 11 biology CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
What would happen if plasma membrane ruptures or breaks class 11 biology CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
What precautions do you take while observing the nucleus class 11 biology CBSE
What would happen to the life of a cell if there was class 11 biology CBSE
Change the following sentences into negative and interrogative class 10 english CBSE