You are a highly experienced educational content creator  for Indian competitive exams such as Railway (Typist - Non_Technical_Posts) under the subject of Mathematics. The topic is **Number System**.. Your task is to generate a detailed **bilingual explanation (English + Hindi)** for a **mnemonic anagram letter** for topic Number System, using the following inputs.

    Generate a Markdown output using this structure:

    ---

    🧠 **Anagram (Short)**: DIVERSES  
    📖 **Expanded (English)**: Diverse Important Various Essential Rational Subtopics Encompassing Simple Elements  
    📖 **Expanded (Hindi)**: विविध महत्वपूर्ण विभिन्न आवश्यक तार्किक उपविषय सरल तत्वों को समेटे हुए

    ---

    ### 🔠 Letter: V / वि — *Venn Diagram Based Problems / वेन आरेख आधारित समस्याएं*

    #### 📚 Concept:
    - EN: Venn Diagram Problems  
    - HI: वेन आरेख समस्याएं

    #### 🧠 Type:
    - EN: Venn Diagram Based Problems  
    - HI: वेन आरेख आधारित समस्याएं

    #### 📖 Description:
    - EN: Using Venn diagrams to solve problems involving sets and overlaps of number properties.  
    - HI: वेन आरेख का प्रयोग करके सेट्स और संख्याओं के गुणों के ओवरलैप की समस्या।

    #### 📌 Explanation:
    - EN: Venn diagrams visually represent sets and their intersections. They aid in calculating overlapping and exclusive groups in number categories.  
    - HI: वेन आरेख सेट्स और उनके ओवरलैप को दर्शाते हैं। ये संख्याओं के वर्गों में ओवरलैप और विशेष समूहों की गणना में मदद करते हैं।

    #### ➗ Formula or Relation:
    - EN: **n(A∪B) = n(A) + n(B) - n(A∩B)**  
    - HI: **n(A∪B) = n(A) + n(B) - n(A∩B)**

    #### 💡 Example Questions:
    **ENGLISH:**
    ['In a group of 50 students, 30 like Mathematics, 20 like Science, and 15 like both. Draw a Venn diagram and find how many students like neither subject using set theory and number system fundamentals.', 'Out of 100 numbers, 60 are divisible by 2, 45 by 3, and 30 by both 2 and 3. Using a Venn diagram, find how many are divisible by 2 or 3 only and neither divisible by 2 nor 3.', 'A railway exam question states: In a jar, there are numbers divisible by 4, 6, and 9. If the total numbers are 120, with 50 divisible by 4, 40 by 6, and 30 by 9, and overlaps given, determine how many are divisible by at least one using Venn diagrams.']

    **HINDI:**
    ['50 छात्रों के समूह में, 30 को गणित पसंद है, 20 को विज्ञान पसंद है, और 15 दोनों को पसंद है। वेन आरेख बनाएं और यह ज्ञात करें कि कितने छात्र दोनों में से किसी को भी पसंद नहीं करते हैं।', '100 संख्याओं में से 60 2 से विभाजित हैं, 45 3 से और 30 दोनों 2 और 3 से विभाजित हैं। वेन आरेख का उपयोग करके पता करें कि कितनी संख्या केवल 2 या केवल 3 से विभाजित हैं और कितनी दोनों से विभाजित नहीं हैं।', 'रेलवे परीक्षा प्रश्न: एक जार में 4, 6, और 9 से विभाजित संख्याएँ हैं। कुल संख्या 120 है, जिसमें 50 4 से, 40 6 से, और 30 9 से विभाजित हैं। ओवरलैप के अनुसार, कम से कम एक द्वारा विभाजित संख्याओं की संख्या ज्ञात करें।']

    ---
    object should have:
        - "mnemonic_letter_english", "mnemonic_letter_hindi"
        - "type_english", "type_hindi"
        - "description_english", "description_hindi"
        - "difficulty_level_english", "difficulty_level_hindi"
        - "exam_frequency_english", "exam_frequency_hindi"
        - "time_to_solve_english", "time_to_solve_hindi"
        - "clue_words_english": list of 4-5 identifying keywords/phrases
        - "clue_words_hindi": same in Hindi
        - "what_to_use_english", "what_to_use_hindi"
        - "formula_english", "formula_hindi"
        - "alternative_formulas_english", "alternative_formulas_hindi": list of 2-3 alternative formulas
        - "algorithm_english", "algorithm_hindi": step-by-step string list
        - "quick_method_english", "quick_method_hindi"

        - "example": answer all  the question give as Example Questions.
 
          - Require multi-step calculation or reasoning.
          - NOT be short phrases, fragments, or simplified school-level word problems.each Example Questions should be including:
            - "example_no"
            - "question_english", "question_hindi"
            - "solution_steps_english": step list
            - "solution_steps_hindi": step list
            - "answer_english", "answer_hindi"
            - "verification_english", "verification_hindi"

        - "variations_english", "variations_hindi": list of variation types
        - "related_concepts_english", "related_concepts_hindi": related subtopics or concepts
        - "common_mistakes_english", "common_mistakes_hindi": list of 10 traps or errors
        - "tip_english", "tip_hindi": short-cut or important tip
        - "prerequisite_knowledge_english", "prerequisite_knowledge_hindi": list of 3 concepts
        - "practice_problems_english", "practice_problems_hindi": list of 3  full-length and detailed practical, compact competitive-level example questions** per type.  
      ⚠️ NOTE : Ensure answer all the question of Example Questions in the example key

        Use simple, learner-friendly language and return only the JSON object in your response, formatted with proper indentation and structure.
        Use clear language suitable for aptitude learners and format the JSON cleanly

### 🔁 output JSon should be

```json
            { 
              "mnemonic_letter_english": "",
              "mnemonic_letter_hindi": "",
              "type_english": "",
              "type_hindi": "",
              "description_english": "",
              "description_hindi": "",
              "difficulty_level_english": "",
              "difficulty_level_hindi": "",
              "exam_frequency_english": "",
              "exam_frequency_hindi": "",
              "time_to_solve_english": "",
              "time_to_solve_hindi": "",
              "clue_words_english": [
                  "",
                  "",
                  "",
                  "",
                  ""
              ],
              "clue_words_hindi": [
                  "",
                  "",
                  "",
                  "",
                  ""
              ],
              "what_to_use_english": "",
              "what_to_use_hindi": "",
              "formula_english": "",
              "formula_hindi": "",
              "alternative_formulas_english": [
                  "",
                  ""
              ],
              "alternative_formulas_hindi": [
                  "",
                  ""
              ],
              "algorithm_english": [
                  "",
                  "",
                  "",
                  ""
              ],
              "algorithm_hindi": [
                  "",
                  "",
                  "",
                  ""
              ],
              "quick_method_english": "",
              "quick_method_hindi": "",
              "example": [
                  {
                  "example_no":"",
                  "question_english": "",
                  "question_hindi": "",
                  "solution_steps_english": [
                      "",
                      "",
                      "",
                      "",
                      ""
                  ],
                  "solution_steps_hindi": [
                      "",
                      "",
                      "",
                      "",
                      ""
                  ],
                  "answer_english": "",
                  "answer_hindi": "",
                  "verification_english": "",
                  "verification_hindi": ""
              }..,],
              "variations_english": [
                  "",
                  "",
                  ""
              ],
              "variations_hindi": [
                  "",
                  "",
                  ""
              ],
              "related_concepts_english": [
                  "",
                  "",
                  ""
              ],
              "related_concepts_hindi": [
                  "",
                  "",
                  ""
              ],
              "common_mistakes_english": [
                  "",
                  ""
              ],
              "common_mistakes_hindi": [
                  "",
                  ""
              ],
              "tip_english": "",
              "tip_hindi": "",
              "prerequisite_knowledge_english": [
                  "",
                  "",
                  ""
              ],
              "prerequisite_knowledge_hindi": [
                  "",
                  "",
                  ""
              ],
              "practice_problems_english": [
                  "",
                  ""
              ],
              "practice_problems_hindi": [
                  "",
                  ""
              ]
          }