If a set is defined as {x | x is a positive integer and x is a divisor of 12}, w

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Question: If a set is defined as {x | x is a positive integer and x is a divisor of 12}, which of the following is NOT an element of this set?

Options:

Correct Answer: 5

Solution:

The divisors of 12 are 1, 2, 3, 4, and 6, so 5 is not an element of this set.

If a set is defined as {x | x is a positive integer and x is a divisor of 12}, 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 divisor of 12}, which of the following is NOT an element of this set?

Step 1: Understand what a divisor is. A divisor of a number is a number that can divide that number without leaving a remainder.
Step 2: Identify the number we are interested in, which is 12.
Step 3: List all the positive integers that can divide 12 evenly. These are the divisors of 12.
Step 4: The divisors of 12 are: 1, 2, 3, 4, 6, and 12.
Step 5: Now, look at the options given in the question to find which number is NOT a divisor of 12.
Step 6: Check each option against the list of divisors. If the number is not in the list, it is NOT an element of the set.
Step 7: In this case, if 5 is one of the options, it is not in the list of divisors, so 5 is NOT an element of the set.

Divisors of a Number – Understanding what divisors are and how to identify them for a given number.
Set Notation – Interpreting set-builder notation to define a set based on specific criteria.
Positive Integers – Recognizing the definition of positive integers and their role in the context of the problem.