Question

Let A={1,2,3,4,...,45} and R be the relation defined as

“is square of a number” on A. Write R as a subset of A×A

.Also, find the domain and range of R.​

Answer 1

Step-by-step explanation:

R is a square of A×A

A×A = { (1,1) , (2,4) , (3,9) , (4,16) , (5,25) , (6,36) }

Domain = {1 , 2 ,3 ,4, 5, 6,....... }

Range = { (1,1) , (2,4) , (3,9) , (4,16) , (5,25) , (6,36) }

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Answer 2

Answer:

Domain of R = {1,2,3,4,5,6}

Range of R = {1,4,9,16,25,36}

Step-by-step explanation:

To find: domain and range

Given: Let A = {1,2,3,4,...,45} and R be the relation.

Solution:

A = {1,2,3,4,...,45}

Now, R be the relation defined as "is square of a number on A"

Then, 1 R 1 [ ∵ $1^{2}$ = 1 ]

          2 R 4 [ ∵ $2^{2}$ = 4 ]

Similarly, 3 R 9, 4 R 16, 5 R 25, 6 R 36

Thus, R = { (1, 1), (2, 4), (3, 9), (4, 16), (5, 25), (6, 36)}

Now, R ∈ A × A

Then R ≤ A × A

R is a subset of A × A

∴ Domain of R = {1,2,3,4,5,6}

∴ Range of R = {1,4,9,16,25,36}, Ans

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