Study the following figure and answer the question given below.
Which of the following statements is true?
I. There are 2354 unmarried literate persons.
II. There are 1513 not literate working persons.}
Show Hint
To find the count for "A but not B", simply sum all numbers inside shape A that do not fall into the overlapping region with shape B.
Step 1: Understanding the Question:
The diagram consists of four overlapping shapes:
Hexagon (Left): Married Female
Hexagon (Right): Married Male
Square (Top): Working
Triangle (Bottom): Literate
We need to calculate the counts for specific groups based on the given statements. Step 2: Detailed Explanation: Analyze Statement I: "There are 2354 unmarried literate persons."
Unmarried Literate Persons: This refers to people who are in the "Literate" set (Triangle) but NOT in the "Married" sets (Left Hexagon or Right Hexagon).
We sum the numbers inside the Triangle excluding any intersections with the Hexagons.
Relevant regions inside the Triangle:
1. Only in Triangle (Literate only): 2003
2. Intersection of Triangle and Square (Literate + Working, but not Married): 367
Calculation: \(2003 + 367 = 2370\).
The statement claims there are 2354 persons.
Since \(2370 \neq 2354\), Statement I is False.
Analyze Statement II: "There are 1513 not literate working persons."
Not Literate Working Persons: This refers to people who are in the "Working" set (Square) but NOT in the "Literate" set (Triangle).
We sum the numbers inside the Square excluding any intersections with the Triangle.
Relevant regions inside the Square:
1. Only in Square (Working only): 1003
2. Intersection of Square and Left Hexagon (Working + Married Female, not Literate): 154
3. Intersection of Square and Right Hexagon (Working + Married Male, not Literate): 356
Calculation: \(1003 + 154 + 356 = 1513\).
The statement claims there are 1513 persons.
Since \(1513 = 1513\), Statement II is True.
Step 3: Final Answer:
Only Statement II is true.
