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List the members of these sets.
a.{x | x is a real number such that x2 = 1}
b.{x | x is a positive integer less than 12}
c.{x | x is the square of an integer and x < 100}
d.{x | x is an integer such that x2 = 2}

Respuesta :

Edufirst
a.{x | x is a real number such that x^2 = 1}

x^2 = 1 => x = +/- 1

=> {-1, 1} <------ answer

b.{x | x is a positive integer less than 12}

1 ≤ x < 12 => {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} <------ answer

c.{x | x is the square of an integer and x < 100}

x = n^2 < 100 => n^2 - 100 < 0

=> (n - 10) (n + 10) < 0

=> a) n - 10 > 0 and n + 10 < 0  => n > 10 and n < - 10 which is not possible

b) n - 10 < 0 and n + 10 > 0 => n < 10 and n > - 10 => - 10 < n < 10

=> n = { - 9, - 8, - 7, - 6, - 5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

=> x = {0, 1, 4, 9, 16, 25, 36, 49, 64, 81} <---- answer

d.{x | x is an integer such that x^2 = 2}

x =  {∅ } because x is √2 which is not an interger but an irrational number

=> Answer: { ∅ }
facundo3141592

The sets are:

  • a) {-1, 1}
  • b) {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}
  • c) {1, 4, 9, 16, 25, 36, 49, 64, 81}
  • d) {∅}.

How to find the elements of each set?

We need to find all the values of x that meet the given restrictions for each set.

a) Here we know that x is a real number and we must have:

x^2  = 1

Solving for x:

x = ±√1 = ±1

Then this set is:

{-1, 1}

b) Here x is a positive integer smaller than 12, this is just:

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}

c) In this case x is a square number, and it must be smaller than 100, so let's find all the square values smaller than 100.

  • 1^2 = 1
  • 2^2 = 4
  • 3^2 = 9
  • 4^2 = 16
  • 5^2 = 25
  • 6^2 = 36
  • 7^2  = 49
  • 8^2 =  64
  • 9*9 = 81
  • 10*10 = 100  (from this onwards, the squares don't meet the criteria).

Then this set is:

{1, 4, 9, 16, 25, 36, 49, 64, 81}

d) Here x must be an integer, such that x^2 = 2

Solving the equation we get:

x = ±√2

But √2 is an irrational number, so there is no integer number that meets this restriction, this means that we have an empty set, this is written as:

{∅}.

If you want to learn more about sets, you can read:

https://brainly.com/question/1563195

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