Question

Write the following
set in roster form.
A = { x: x is a natural number and x
${x}^{2}$
<40}​

Answer 1

Given

Set builder form =>

A = {x : x is a natural number and x² < 40}

As first statement clears,

x is a natural number

which means that value of x can be 1 to infinity because Natural numbers lie 1 to infinity.

Also given,

x² < 40

x < √40

x < 6.324

Since x < 6.324 and a natural number as well

So x can have possible values of 1,2,3,4,5 and 6.

Alternate way

x² < 40

Putting x = 1 to x = infinity (Hit and trial method)

Taking x = 1, x² = 1² = 1 < 40      which is true

Taking x = 2, x² = 2² = 4 < 40     which is true

Taking x = 3, x² = 3² = 9 < 40     which is true

Taking x = 4, x² = 4² = 16 < 40     which is true

Taking x = 5, x² = 5² = 25 < 40     which is true

Taking x = 6, x² = 6² = 36 < 40     which is true

Taking x = 7, x² = 7² = 49 < 40      which is false

Thus x will have value less than 7

i.e, x = 1 to 6

Thus, x can have value = 1,2,3,4,5 and 6

Thus roster form is

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

Answer 2

$\huge {\purple{ \underline{ \underline{\mathbb{ANSWER}}}}}$

Given

Set builder form =>

A = {x : x is a natural number and x² < 40}

As first statement clears,

x is a natural number

which means that value of x can be 1 to infinity because Natural numbers lie 1 to infinity.

Also given,

x² < 40

x < √40

x < 6.324

Since x < 6.324 and a natural number as well

So x can have possible values of 1,2,3,4,5 and 6.

Alternate way

x² < 40

Putting x = 1 to x = infinity (Hit and trial method)

Taking x = 1, x² = 1² = 1 < 40      which is true

Taking x = 2, x² = 2² = 4 < 40     which is true

Taking x = 3, x² = 3² = 9 < 40     which is true

Taking x = 4, x² = 4² = 16 < 40     which is true

Taking x = 5, x² = 5² = 25 < 40     which is true

Taking x = 6, x² = 6² = 36 < 40     which is true

Taking x = 7, x² = 7² = 49 < 40      which is false

Thus x will have value less than 7

i.e, x = 1 to 6

Thus, x can have value = 1,2,3,4,5 and 6

Thus roster form is

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