If a set is defined as {x | x is a positive integer and x is a multiple of 3}, w

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Question: If a set is defined as {x | x is a positive integer and x is a multiple of 3}, which of the following is NOT an element of this set?

Options:

Correct Answer: 10

Solution:

The number \'10\' is not a multiple of 3, hence it is not an element of the set.

If a set is defined as {x | x is a positive integer and x is a multiple of 3}, which of the following is NOT an element of this set?

If a set is defined as {x | x is a positive integer and x is a multiple of 3}, which of the following is NOT an element of this set?

Step 1: Understand what the set is. The set is defined as {x | x is a positive integer and x is a multiple of 3}. This means we are looking for positive integers that can be divided by 3 without leaving a remainder.
Step 2: Identify what a multiple of 3 is. A multiple of 3 is any number that can be expressed as 3 times another whole number. For example, 3, 6, 9, 12, etc. are all multiples of 3.
Step 3: Check the number '10'. We need to see if 10 is a multiple of 3. To do this, divide 10 by 3.
Step 4: Perform the division. When you divide 10 by 3, you get 3 with a remainder of 1. This means 10 cannot be expressed as 3 times a whole number.
Step 5: Conclude that since 10 is not a multiple of 3, it is not an element of the set.

Set Definition – Understanding how sets are defined using set-builder notation, specifically focusing on the criteria for membership in the set.
Multiples of a Number – Identifying multiples of a given number, in this case, 3, and recognizing which integers fit this criterion.
Positive Integers – Recognizing the subset of integers that are positive and understanding their properties.