Answer :
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.
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