1

Problem

Use a Venn diagram to represent the sets of factors of 12, even numbers, and numbers less than 13. Then determine which numbers belong to each set. Based on your diagram, decide whether the statement “The only positive factors of 12 that are less than 13 and not even are 1 and 3” is true or false. Explain your reasoning.

2

Step

Identify each set

Set A (factors of 12) = {1, 2, 3, 4, 6, 12}
Set B (even numbers) less than 13 = {2, 4, 6, 8, 10, 12}
Set C (numbers less than 13) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

3

Step

Find the intersection — numbers that are in all relevant sets
We’re interested in numbers that are:

Factors of 12Less than 13 Not even

4

Step

So start with factors of 12 that are less than 13 (that’s all of them) and remove the even ones:

{1, 2, 3, 4, 6, 12}
Even numbers from this list = {2, 4, 6, 12}
Remaining (not even) = {1, 3}

5

Step

Evaluate the statement, The statement says:
“The only positive factors of 12 that are less than 13 and not even are 1 and 3.”

We found that the non-even (odd) factors are indeed 1 and 3.
The statement is TRUE.

6

Step

Explain using the imagined Venn diagram
If you imagine the Venn diagram:

The circle for “factors of 12” overlaps with “even numbers” at {2, 4, 6, 12}.
The overlap between “factors of 12” and “numbers less than 13” includes all the factors.
The part of the “factors of 12” circle outside the “even numbers” circle (but still within numbers less than 13) has 1 and 3.

7

Solution

Thus, those are the only ones satisfying all conditions

8

Sumup

Please summarize Problem, Clue, Hint, Formula, Steps and Solution

Choices

9

Choice-A

Although 1 and 3 are odd, 5 is not a factor of 12 (since 12 ÷ 5 = 2.4, not a whole number). So this option is wrong.

Wrong False, because 1, 3, and 5 are all odd factors of 12.

10

Choice-B

3 is a factor of 12, but 9 is not (12 ÷ 9 = 1.33). Also, it ignores 1, which is a factor and not even. So this statement is false.

Wrong False, because 3 and 9 are the only factors of 12 that are not even.

11

Choice-C

This option correctly identifies 1 and 3 as the only factors of 12 that are odd (not even) and less than 13. It matches the reasoning and is completely accurate.

Correct True, because 1 and 3 are the only factors of 12 that are odd and less than 13.

12

Choice-D

Not all factors of 12 are even — 1 and 3 are odd. Therefore, the reasoning in this option is wrong.

Wrong True, because all factors of 12 are even numbers.

13

Answer

Option

C

14

Sumup

Please summarize choices