FormulaHub/relations.html at main · NawazHaider/FormulaHub · GitHub

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<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8" />
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  <title>Chapter 2: Relations & Functions</title>
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  <div class="chapter-header">
    <h1>Chapter 2: Relations & Functions – Formula Sheet</h1>
  </div>

  <div class="formula-box">
    <strong>Cartesian Product:</strong>
    \( A \times B = \{(a, b) \mid a \in A, b \in B\} \)
  </div>

  <div class="formula-box">
    <strong>Relation:</strong>
    A relation \( R \) from set \( A \) to \( B \) is a subset of \( A \times B \)
  </div>

  <div class="formula-box">
    <strong>Domain & Range:</strong>
    - Domain: Set of first elements in relation
    - Range: Set of second elements
  </div>

  <div class="formula-box">
    <strong>Function:</strong>
    A relation in which every element of \( A \) maps to exactly one element in \( B \)
  </div>

  <div class="formula-box">
    <strong>Types of Functions:</strong>
    <ul>
      <li>One-one (Injective): Different inputs map to different outputs</li>
      <li>Onto (Surjective): Every element in codomain is mapped</li>
      <li>Bijective: Both one-one and onto</li>
    </ul>
  </div>
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