Step 1: Find the elements that can be related.
The rule is $y = 3x$ with $y$ at most 16. So $x$ can only be a natural number with $3x \leq 16$. Testing values, $x=5$ gives 15, and $x=6$ gives 18, which is outside $A$. So $x$ runs from 1 to 5.
Step 2: Write domain and range.
Domain is the set of allowed $x$: $\{1,2,3,4,5\}$. Range is the set of the values $3x$: $\{3,6,9,12,15\}$. So A and B are both correct.
Step 3: Test reflexive with one element.
A reflexive relation must contain $(a,a)$ for all $a$, so $a = 3a$ would be needed. That holds only for $a=0$, and 0 is not in $A$. So $R$ is not reflexive and C is wrong.
Step 4: Test symmetric with one pair.
Take $(1,3)$. Its reverse is $(3,1)$. Since $1 \neq 3\times 3$, the reverse pair is missing. So $R$ is not symmetric and D is correct.
Step 5: Read off the answer.
Correct statements: A, B, D. Only option 4 lists exactly these.
Step 6: Cross check with a count.
The relation has exactly 5 ordered pairs, one for each $x$ from 1 to 5, because the map $x \to 3x$ is one-one. A relation with 5 pairs cannot be reflexive on a 16 element set, since reflexive needs at least 16 pairs. This agrees with C being false. Also, $R$ sends 1 to 3, and 3 to 9, so the reverse pairs cannot be present. This agrees with D being true.
Final Answer:
The correct statements are A, B and D.
\[ \boxed{\text{Option 4}} \]