🌟 Quick Verification

• Direct Answer: The correct answer is Both (A) and (R) are true, and (R) is the correct explanation of (A).
• Core Concept: [Hierarchical Set Modeling] represents multiple independent sub-entities inside a single encompassing category.

🧠 Solution Blueprint

• Assertion Verification: Fairies and unicorns are separate mythical creatures, depicted as two distinct circles inside a larger parent circle.
• Reason Verification: The reason accurately explains the logical principle that separate sub-categories under a common parent are modeled as independent subsets.

🌟 Quick Verification

• Direct Answer: The correct answer is A-2, B-3, C-4, D-1.
• Core Concept: Matching specific set populations to given numerical data.

🧠 Solution Blueprint

• Matching Details:
  • Players who are neither artists nor doctors equals 25 (A-2).
  • Doctors who are both players and artists equals 3 (B-3).
  • Doctors who are neither players nor artists equals 27 (C-4).
  • Artists who are neither players nor doctors equals 30 (D-1).

All pigeons are birds, but dogs are not birds. Therefore, there will be a large circle of birds containing a small circle of pigeons, and the circle for dogs will be separate. This is shown in option (E).

The correct Venn-diagram for Carrot, Food, and Vegetables is option (B) because all carrots are vegetables and all vegetables are food.

Statements like 'Some shirts are towels' and 'Some towels are gloves' create a chain of partial overlaps where adjacent categories intersect, but non-adjacent ones may not necessarily intersect directly.

In the intersection of educated (triangle) and male (square), the number '11' is outside the urban (circle) region.

Educated dancers have been shown by the common region of triangle and rectangle (Wait, checking logic in image, the region common to triangle and square for educated dancers is 4+2+1). Educated dancers = 4+2+1=7.

To identify a group consisting exclusively of specific categories such as dogs, fishes, and mongooses, one must locate the common intersection region occupied by symbols A, C, and D.

According to the diagram, the value 200 is given for the Hindi circle, which represents the 'only Hindi' region.

These three categories can partially overlap because an individual can be illiterate, poor, and unemployed all at once. Diagram C shows the intersection.

The intersection region of Physics and Chemistry contains students who study both Physics and Chemistry. To exclude those studying Mathematics, we select the part outside the Mathematics circle. According to the question, the correct answer is 9.

Shirts, bedsheets, and towels are all distinct textile products with no overlapping relationship. Diagram A has three separate circles.

Lucknow is located in the state of Uttar Pradesh (UP), while Madhya Pradesh (MP) is a separate state. Therefore, in the Venn-diagram, there will be a larger circle for 'Uttar Pradesh' containing a smaller circle for 'Lucknow', and a separate circle for 'Madhya Pradesh'.

🌟 Quick Verification

• Direct Answer: The correct answer is 15 only cricket, 20 only football.
• Core Concept: [Venn Diagram Set Calculations] use set subtraction to isolate single-category preferences.

🧠 Solution Blueprint

• Step-by-Step Calculation:
  • Total cricket fans = 50.
  • Students liking both cricket and football = 35.
  • Students liking only cricket = Total cricket fans minus those who like both ($50 - 35 = \mathbf{15}$).
  • Total students = 70, so total football fans = Total students minus cricket-only fans minus both fans ($70 - 15 - 35 = \mathbf{20}$). Alternatively, students liking only football = Total students minus total cricket fans ($70 - 50 = \mathbf{20}$).

🌟 Quick Verification

• Direct Answer: The correct answer is They are a teacher or graduate and not a politician.
• Core Concept: Intersection and complement operations across geometric sets.

🧠 Solution Blueprint

• Step-by-Step Reasoning:
  • Being inside the small triangle means being a teacher.
  • Being inside the circle means being a graduate.
  • Being outside the large triangle means excluding politicians.
  • Combining these rules shows that such individuals fit the description of being a teacher or graduate while not being a politician.

The total count of red cars is obtained by summing all the numerical values located within the designated 'Red Cars' region: 14 + 5 + 8 + 6 equals 33.

The number '5' is located in the intersection of Qualified (Triangle), Experienced (Square), and Doctors working in Village (Circle).

Educated boys have been shown by the common region of triangle and square. Number of educated boys = 3+4=7. Now, we have to find such educated boys who are not dancers. Therefore, we have to subtract that common region which includes rectangle. Hence, the number of educated boys who are not dancers = 7-4 = 3.

Both husband and wife are members of a family, but they are distinct (opposite) from each other. Thus a large circle 'Family' and two separate circles 'Husband' and 'Wife' inside it.

🌟 Quick Verification

• Direct Answer: The correct match is A-1, B-2, C-3, D-4.
• Core Concept: [Multi-Shape Analysis Diagrams] assign specific geometric figures to distinct demographic or professional groups.

🧠 Solution Blueprint

• Step-by-Step Verification:
  • Small Triangle represents Teachers.
  • Large Triangle represents Politicians.
  • Circle represents Graduates.
  • Rectangle represents Members of Parliament.