Use the Venn diagrams you drew in Exercises 1 – 3 to decide whether the statement is true or false. Explain your reasoning. The only positive factors of 12 less than 13 that are not even are 1 and 3.

Identify the positive factors of 12:
→ The positive factors of 12 are the numbers that divide 12 without leaving a remainder
→ The positive factors of 12 are: 1, 2, 3, 4, 6, and 12

Identify the factors less than 13:
→ All the positive factors of 12 (1, 2, 3, 4, 6, 12) are already less than 13, so we don’t exclude any factors in this step

Identify the even factors:
→ Even factors among the positive factors of 12 are: 2, 4, 6, and 12

Identify the factors that are not even:
→ The factors of 12 that are not even are: 1, 3

State the factors of 12 that are less than 13 and are not even:
→ From the steps above, the factors of 12 that are less than 13 and are not even are: 1, 3

Therefore, the statement "The only positive factors of 12 less than 13 that are not even are 1 and 3" is true.

This option would be correct if other factors of 12 are not even and less than 13, but our analysis shows that only 1 and 3 fit the criteria. Therefore, this option is incorrect

FALSE

This option is ambiguous and does not clearly state what "both" refers to. In the context of binary truth values (true or false), "both" is not a standard answer. Therefore, this option does not apply to the problem

Both

This option is correct because our analysis confirms that the statement is accurate. The only positive factors of 12 that are less than 13 and not even are indeed 1 and 3

TRUE

This option would be correct if none of the other options were suitable. Since option 3 is the correct answer, this option is incorrect

None of this

Option

C

Can you summarize what you’ve understood in the above steps?