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Denote the set below by set-builder notation, using x as the variable.
{1,3,5, ..., 67}
Choose the correct answer below.
O A. {x|x is even natural numbers less than 68}
B. {x|x is an odd natural number less than 68}
C. {x|x is an odd natural number between 1 and 67}
D. {x|x is an odd natural number greater than 1}

Sagot :

really226

Answer:

C. {x|x is an odd natural number between 1 and 67}

Step-by-step explanation:

B and C is also correct if the natural number is defined to be started with 1: positive integer,

but if it's defined to be non-negative real number then only C

Set-builder notation of the given set is  {[tex]x | x[/tex] is an odd natural number less than [tex]68[/tex]}.

What is set?

" Set is defined as the collection of the given object with certain properties."

According to the question,

Given set,

[tex]\{1,3,5, ..., 67\}[/tex]

[tex]'x'[/tex] represents the variable

A. {[tex]x | x[/tex] is an even natural numbers less than [tex]68[/tex]}.

Even numbers are multiple of 2, given set does not represents set of even numbers.

Option(A) is not the correct answer.

B. { [tex]x | x[/tex] is an odd natural number less than [tex]68[/tex]}.

[tex]\{1,3,5, ..., 67\}[/tex] represents set of odd numbers , all numbers are less than 68.

Hence, Option (B) is the correct answer.

C. {[tex]x |x[/tex] is an odd natural number between [tex]1[/tex] and [tex]67[/tex]} means [tex]\{ 3, 5, 7,...., 65\}[/tex]

Here between  [tex]1[/tex] and [tex]67[/tex] excludes  [tex]1[/tex] and [tex]67[/tex]. But in the given set  [tex]1[/tex] and [tex]67[/tex]

are included.

Option (C) is not the correct answer.

D.  {[tex]x |x[/tex] is an odd natural number greater than [tex]1[/tex]} means [tex]\{ 1, 3, 5,...........\}[/tex]

Here this set goes till infinity.

Option (D) is not the correct answer.

Hence, Option (B) is the correct answer.

Learn more about set here

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