Question

Which set of numbers includes only integers? Left-brace 14, 9, one-third, 0, 243 Right-brace Left-brace 14, negative 7, 0, 243, negative 3 Right-brace Left-brace 14, Negative StartFraction 9 Over 10 EndFraction, 56, 0, negative 243 Right-brace Left-brace 14, 2.3, 654, 0, 9 Right-brace

Answer 1

GIVEN :

Which set of numbers includes only integers?

A) ${\{14, 9,\frac{1}{3},0,243}\}$

B) ${\{14, -7, 0, 243, -3}\}$

C) ${\{14, -\frac{9}{10},56,0,-243}\}$

D) ${\{14, 2.3, 654, 0, 9}\}$

TO FIND :

The set of numbers includes only integers

SOLUTION :

Given that the four options are

A) ${\{14, 9,\frac{1}{3},0,243}\}$

B) ${\{14, -7, 0, 243, -3}\}$

C) ${\{14, -\frac{9}{10},56,0,-243}\}$

D) ${\{14, 2.3, 654, 0, 9}\}$

We have to find the set of numbers includes only integers.

The set  formed by the negative integers, zero and the positive integers  is called the set of integers.

It can be denoted by the symbol Z and can be written as below

$Z={\{...,-2,-1,0,1,2,...}\}$

When we comparing the definition of integers with the options we have that

A) ${\{14, 9,\frac{1}{3},0,243}\}$

In the above set there is a rational number $\frac{1}{3}$ and it is not included in the set of integers (by defintion)

B) ${\{14, -7, 0, 243, -3}\}$

In the above set there negative integers, zero and positive integers all are belongs to the set of integers (by defintion)

⇒ option B)  ${\{14, -7, 0, 243, -3}\}$ is correct

∴ the set of numbers includes only integers is ${\{14, -7, 0, 243, -3}\}$

Answer 2

b Step-by-step explanation: