Question

Suppose $\bigcup _ { i = 1 } ^ { 30 } A _ { i } = \bigcup _ { j = 1 } ^ { n } B _ { j }$= S and each elements of S belongs to exactly 10 of the and exactly 9 of the . Then n is equal to

• A. 15
• B. 3
• C. 45
• D. None of these

Answer 1

Answer: (C)

45

Answer 2

O(S) = $O \left( \bigcup _ { i = 1 } ^ { 30 } A _ { i } \right) = \frac { 1 } { 10 } ( 5 \times 30 ) = 15$Since, element in the union S belongs to 10 of A_i^' s

Also, O(S) = $O \left( \bigcup _ { j = 1 } ^ { n } B _ { j } \right) = \frac { 3 n } { 9 } = \frac { n } { 3 }$ , ∴ $\frac { n } { 3 } = 15 \Rightarrow n = 45$.