Question

let A = {1,2,3,4,......45} and R be the relation defined as " is square of " in A. write R as a subset of A cross A. also find its domain and range of R

Answer 1

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}

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}

Answer 2

Answer:

Step-by-step explanation:

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

Let "A" be a set which contains some of elements of A

$A=\{1, 2, 3, 4, 5, 6\}$

Now, we have to write the other set of elements from A. The elements in this set denotes the square value of previous set.

Square values of set $A=\{1, 4, 9, 16, 25, 36\}$

$A\times{A}=\{(1, 1)(1,4)(1, 9)(1, 16) (1, 25)  (1, 36)..................\}$

Therefore,

$\text{Domain}=\{1, 2, 3, 4, 5, 6\}$

$\text{Range}=\{1, 4, 9, 16, 25, 36\}$