Answer

Verified

374.7k+ views

**Hint**: According to given in the question we have a se i.e. $ A = \left\{ {1,2,3,...45} \right\} $ . We have to find the relation and domain. Let us first know what is the definition of Domain. The domain of the function is the complete set of possible values of the independent variables. So we have to find all the possible values i.e. the square of all the numbers in the function which is the relation of A .

**Complete step-by-step answer**:

Here we have $ A = \left\{ {1,2,3,...45} \right\} $ and R be the relation ‘Is square of’ in A.

To find the R we can write $ {(1)^2} = 1,{(2)^2} = 4,{(3)^2} = 9,{(4)^2} = 16,{(5)^2} = 25,{(6)^2} = 36 $ .

Therefore we have $ R = \left\{ {(1,1),(4,2),(9,3),(16,4),(25,5),(36,6)} \right\} $ .

From the definition we know that Domain of $ R = \left\{ {x;(x,y) \in R} \right\} = \left\{ {1,4,9,16,25,36} \right\} $

So we can write a range of $ $ $ R = \left\{ {y;(x,y) \in R} \right\} = \left\{ {1,2,3,4,5,6} \right\} $ .

We can see that all the options given in the question match the solution except (d).

Hence we can say that option (d) is false.

**So, the correct answer is “Option d”.**

**Note**: We should note that the definition of Range says that the range of a function is the complete set of all possible values of the dependent variable i.e. $ y $ after we have substituted the domain. So in the above solution we have first substituted the domain of $ R $ and then the range of $ R $ . We have here $ x = 1,4,9,16,25,36 $ and for variable $ y = $ $ 1,2,3,4,5,6 $ .

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

Which are the Top 10 Largest Countries of the World?

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

How do you graph the function fx 4x class 9 maths CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths