# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-10/18

Exercises: Try Out - Set 10: Real exam simulation to sharpen your skills and build confidence. - Intersection of Two Sets

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## Exercise 18

### Question

export const metadata = {
  title: "Intersection of Two Sets",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/27/2025",
};

Given two sets:

<MathContainer>
  <BlockMath math="A = \{x | -3 < x < 8, x \in \text{integers}\}" />
  <BlockMath math="B = \{x | x \leq 7, x \in \text{integers}\}" />
</MathContainer>

The intersection of these two sets is...


### Choices

- [ ] $$\{x | -3 \leq x, x \in \text{integers}\}$$
- [ ] $$\{x | -3 < x, x \in \text{integers}\}$$
- [ ] $$\{x | x \leq 7, x \in \text{integers}\}$$
- [x] $$\{x | -3 < x \leq 7, x \in \text{integers}\}$$
- [ ] $$\{x | -3 < x < 7, x \in \text{integers}\}$$

### Answer & Explanation

export const metadata = {
  title: "Set Intersection Explanation",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/27/2025",
};

First, let's list the members of set <InlineMath math="A" />. Set <InlineMath math="A" /> contains integers between <InlineMath math="-3" /> and <InlineMath math="8" /> (exclusive):

<MathContainer>
  <BlockMath math="A = \{-2, -1, 0, 1, 2, 3, 4, 5, 6, 7\}" />
</MathContainer>

Next, set <InlineMath math="B" /> contains all integers less than or equal to <InlineMath math="7" />:

<MathContainer>
  <BlockMath math="B = \{..., -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7\}" />
</MathContainer>

The intersection of two sets (<InlineMath math="A \cap B" />) is the set containing elements that are present in both sets.

Since all members of set <InlineMath math="A" /> (from <InlineMath math="-2" /> to <InlineMath math="7" />) are also contained in set <InlineMath math="B" />, the intersection is set <InlineMath math="A" /> itself:

<MathContainer>
  <BlockMath math="A \cap B = \{-2, -1, 0, 1, 2, 3, 4, 5, 6, 7\}" />
</MathContainer>

Converting this back to set-builder notation, the elements are integers greater than <InlineMath math="-3" /> and less than or equal to <InlineMath math="7" />:

<MathContainer>
  <BlockMath math="A \cap B = \{x | -3 < x \leq 7, x \in \text{integers}\}" />
</MathContainer>


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