Question

{x:x is an integer, x3≤100} in roster form

Answer 1

SOLUTION :

TO EXPRESS

The set {x:x is an integer, x3≤100} in roster form

CONCEPT TO BE IMPLEMENTED

SET :

A set is a well defined collection of distinct objects

REPRESENTATION OF SET

A set can be represented in following ways

• Set Builder form
• Tabular or Roster form

EVALUATION

The given set is

$\sf{} \{ \: x : x \: is \: an \: integer \: , \: {x}^{3} \leqslant 100 \: \}$

Here

$\sf{}For \: \: x = 0 \: , \: {0}^{3} = 0 \leqslant 100$

$\sf{}For \: \: x = 1 \: , \: {1}^{3} = 1 \leqslant 100$

$\sf{}For \: \: x = 2 \: , \: {2}^{3} = 8 \leqslant 100$

$\sf{}For \: \: x = 3 \: , \: {3}^{3} = 27 \leqslant 100$

$\sf{}For \: \: x = 4 \: , \: {4}^{3} = 64 \leqslant 100$

$\sf{}For \: \: x = 5 \: , \: {5}^{3} = 125 > 100$

$\sf{}Also \: for \: any \: negative \: integer \: x \: , \: {x}^{3} \leqslant 100$

Hence the required roster form is

$\sf{} \{ \: 4,3,2,1,0,-1,-2,-3,........ \}$

━━━━━━━━━━━━━━━━

LEARN MORE FROM BRAINLY

If n(A) = 300, n(A∪B) = 500, n(A∩B) = 50 and n(B′) = 350, find n(B) and n(U)

https://brainly.in/question/4193770