Question

Let A={1,2,3,4,...,45} and R be the relation defined as “is square of ” on A. Write R as a subset of A×A. Also, find the domain and range of R.

Answer 1

Answer:

Step-by-step explanation:

Given Let A={1,2,3,4,...,45} and R be the relation defined as “is square of ” on A. Write R as a subset of A×A. Also, find the domain and range of R.

Let P be the set that contains elements of A

So P = {1,2,3,4,5,6,7}

Now we need to write one more set of elements from P.

So square values of set P will be {1,4,9,16,25,36,49}

P x P = {(1,1), (1,4),(1,9),(1,16),(1,25),(1,25),(1,36),(1,49) .......}

So Domain is {1,2,3,4,5,6,7}

Range will be {1,4,9,16,25,36,49}

Answer 2

Answer:

let A = {1,2,3,4,......45} and R be the relation defined as " is square of " in A.

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

Range =  { 1 , 4 , 9 , 16 , 25 , 36}

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

Step-by-step explanation:

R = square of A ∈ A

R = 1²  , 2²  , 3²  , 4²  , 5²  , 6²    ( 7² = 49 > 45)

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

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

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

R ∩ A =  { 1 , 4 , 9 , 16 , 25 , 36}

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