Set Operations on Numbers

Explanation

Let's define the members of each set:

We will check each option to see if the number can be formed by multiplying two members of these sets.

Analysis of Options

1. Option A: $-14$

   $$-14 = (-7) \times 2$$

   Here, $-7 \in A$ and $2 \in B$. So, $-14$ is possible.

2. Option B: $-15$

   $$-15 = (-5) \times 3$$

   Here, $-5 \in A$ and $3 \in C$. So, $-15$ is possible.

3. Option C: $-18$

   $$-18 = (-3) \times 6$$

   Here, $-3 \in A$ and $6 \in B$ (also $6 \in C$). So, $-18$ is possible.

4. Option D: $14$

   $$14 = 2 \times 7$$

   Here, $2 \in B$. However, $7$ is a positive odd integer that is not divisible by $3$. This means:

   • $7 \notin A$ (since $A$ contains negative integers).
   • $7 \notin B$ (since $7$ is odd).
   • $7 \notin C$ (since $7$ is not divisible by $3$).

   Since one of the factors ($7$) is not present in sets $A$, $B$, or $C$, $14$ cannot be formed (assuming the pattern involves factors from different sets or positive factors).

5. Option E: $18$

   $$18 = 2 \times 9$$

   Here, $2 \in B$ and $9 \in C$. So, $18$ is possible.

Therefore, the number that is NOT included in the product is $14$.