# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-7/12

Exercises: Try Out - Set 7: Real exam simulation to sharpen your skills and build confidence. - Problem 12

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## Exercise 12

### Question

export const metadata = {
  title: "Problem 12",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/25/2025",
};

Given an operation on the set of integers defined by the rule <InlineMath math="\beta(w \oplus x \ominus y \otimes z) = 2w + x \cdot y - (-z)" />. The value of <InlineMath math="\beta(2 \oplus 3 \ominus 4 \otimes (-2))" /> is ...


### Choices

- [x] $$14$$
- [ ] $$18$$
- [ ] $$13$$
- [ ] $$9$$
- [ ] $$7$$

### Answer & Explanation

export const metadata = {
  title: "Solution for Problem 12",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/25/2025",
};

Given the operation rule:
<MathContainer>
  <BlockMath math="\beta(w \oplus x \ominus y \otimes z) = 2w + x \cdot y - (-z)" />
</MathContainer>

We are asked to find the value of:
<MathContainer>
  <BlockMath math="\beta(2 \oplus 3 \ominus 4 \otimes (-2))" />
</MathContainer>

By comparing variable positions, we get:
- <InlineMath math="w = 2" />
- <InlineMath math="x = 3" />
- <InlineMath math="y = 4" />
- <InlineMath math="z = -2" />

Substitute these values into the formula:
<MathContainer>
  <BlockMath math="\beta(2 \oplus 3 \ominus 4 \otimes (-2)) = 2(2) + 3 \cdot 4 - (-(-2))" />
  <BlockMath math="= 4 + 12 - (2)" />
  <BlockMath math="= 16 - 2" />
  <BlockMath math="= 14" />
</MathContainer>

Therefore, the value of the operation is <InlineMath math="14" />.


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