The question asks us to identify the set of numbers among the given options that is NOT related in the same way as the example sets: (5, 13, 16) and (4, 11, 14).

We need to find the relationship or pattern that connects the three numbers in each set. Let's denote a set as (a, b, c), where 'a' is the first number, 'b' is the second, and 'c' is the third.

Analysing the Pattern in Example Sets

Let's look at the first example set (5, 13, 16):

• Relationship between 5 and 13: $13 - 5 = 8$. Or $5 \times 2 + 3 = 13$.
• Relationship between 13 and 16: $16 - 13 = 3$.

Let's look at the second example set (4, 11, 14):

• Relationship between 4 and 11: $11 - 4 = 7$. Or $4 \times 2 + 3 = 11$.
• Relationship between 11 and 14: $14 - 11 = 3$.

We observe a consistent pattern in both example sets:

1. The second number (b) is obtained by multiplying the first number (a) by 2 and adding 3: $b = 2a + 3$.
2. The third number (c) is obtained by adding 3 to the second number (b): $c = b + 3$.

Let's verify this pattern with the example sets:

• For (5, 13, 16): $b = 2 \times 5 + 3 = 10 + 3 = 13$ (Correct). $c = 13 + 3 = 16$ (Correct). This set follows the pattern.
• For (4, 11, 14): $b = 2 \times 4 + 3 = 8 + 3 = 11$ (Correct). $c = 11 + 3 = 14$ (Correct). This set also follows the pattern.

So, the pattern is $b = 2a + 3$ AND $c = b + 3$.

Checking the Options Against the Pattern

Now, let's apply this pattern to each of the given options to find the one that does NOT follow both rules.

Option 1: (8, 13, 10)

Here, $a=8$, $b=13$, $c=10$.

• Rule 1: $b = 2a + 3$? $13 = 2 \times 8 + 3 = 16 + 3 = 19$. This is false ($13 \neq 19$).
• Rule 2: $c = b + 3$? $10 = 13 + 3 = 16$. This is false ($10 \neq 16$).

This set does NOT follow either rule of the pattern.

Option 2: (12, 21, 18)

Here, $a=12$, $b=21$, $c=18$.

• Rule 1: $b = 2a + 3$? $21 = 2 \times 12 + 3 = 24 + 3 = 27$. This is false ($21 \neq 27$).
• Rule 2: $c = b + 3$? $18 = 21 + 3 = 24$. This is false ($18 \neq 24$).

This set does NOT follow either rule of the pattern.

Option 3: (7, 17, 20)

Here, $a=7$, $b=17$, $c=20$.

• Rule 1: $b = 2a + 3$? $17 = 2 \times 7 + 3 = 14 + 3 = 17$. This is true ($17 = 17$).
• Rule 2: $c = b + 3$? $20 = 17 + 3 = 20$. This is true ($20 = 20$).

This set follows both rules of the pattern.

Option 4: (9, 21, 26)

Here, $a=9$, $b=21$, $c=26$.

• Rule 1: $b = 2a + 3$? $21 = 2 \times 9 + 3 = 18 + 3 = 21$. This is true ($21 = 21$).
• Rule 2: $c = b + 3$? $26 = 21 + 3 = 24$. This is false ($26 \neq 24$).

This set follows the first rule but fails the second rule of the pattern.

Summary of Pattern Check

Let's summarize the findings in a table:

The example sets and Option 3 follow both rules of the pattern. Options 1 and 2 follow neither rule. Option 4 follows the first rule ($b = 2a + 3$) but not the second rule ($c = b + 3$).

The question asks for the set that is NOT related in the same way as the example sets. While Options 1, 2, and 4 do not fully follow the pattern, Option 4 is uniquely different because it follows one part of the pattern while failing the other, unlike Options 1 and 2 which fail both parts. Therefore, Option 4 is the set that is NOT related in the exact same way as the examples and Option 3.

Conclusion on Number Set Relation

Based on the analysis, the numbers in the sets (5, 13, 16), (4, 11, 14), and (7, 17, 20) share the relationship where the second number is twice the first plus three, and the third number is three more than the second. The set (9, 21, 26) follows the relationship for the second number but not the third, making it the set that is NOT related in the same way.

The final answer is $\boxed{(9, 21, 26)}$.

Revision Table: Number Set Pattern

Review the pattern discovery and application process:

• Identify the pattern based on relationships between numbers in the given example sets.
• Formulate the rules that define the pattern ($b = 2a + 3$, $c = b + 3$).
• Systematically check each option to see if it satisfies both rules.
• Identify the option that deviates from the pattern in a unique way compared to others.

Additional Information: Logical Reasoning

Logical reasoning questions involving number sets often require identifying arithmetic or algebraic relationships between the numbers. Common patterns include arithmetic progressions, geometric progressions, differences between consecutive numbers, sums or products of numbers, or rules based on the position of the number in the set (first, second, third). It's important to test simple patterns first and then look for more complex ones if needed. Carefully reading the question to understand exactly what is being asked (e.g., find the one that IS related or the one that is NOT related) is crucial.