In a survey of 100 students, the number of students studying various languages were found to be: English only-18 English but not Hindi-23 English and German-8 English-26 German-48 German and Hindi-8 No language-24 Then, which of the following statements are true? A. Number of students who were studying Hindi is 18. B. Number of students who were studying English and Hindi is 3. C. Number of students who were studying English, Hindi and German is 3.

This is a Venn diagram problem! We need to organize the given information carefully and work through each statement. First, let's find students studying English AND Hindi: Total English students $= 26$ English but not Hindi $= 23$ Therefore: English AND Hindi $= 26 - 23 = 3$ students Statement B is TRUE Next, let's find students studying English, Hindi AND German: Since only $3$ students study both English and Hindi, and we know that $8$ students study English and German, these $3$ students who study English and Hindi must also be studying German. Therefore: English, Hindi AND German $= 3$ students Statement C is TRUE Finally, let's find total Hindi students: Students studying Hindi come from: - German and Hindi $= 8$ students - But $3$ of these also study English - So German and Hindi only $= 8 - 3 = 5$ students - English and Hindi (all study German too) $= 3$ students - Hindi only $= 18 - 8 = 10$ students Let's verify with total of $100$ students: - English only: $18$ - German only: $48 - 8 = 40$ - Hindi only: $10$ - English & Hindi & German: $3$ - German & Hindi only: $5$ - No language: $24$ - Total: $18 + 40 + 10 + 3 + 5 + 24 = 100$ ✓ Statement A is TRUE All statements A, B, and C are TRUE.