In a group of 15 people, 8 read English, 7 read French while 3 of them read none of these two. How many of them read French and English both?  Choose the correct choice from the following choices.
A) 2 B) 3 C) 4 D) 7 E) 5

Rationale: in the following venn diagram , f and e represent people who read french and english respectively . now , [ f + ( { f ∩ e } ) + e ] = 15 - 3 ( or ) f + e + ( f ∩ e ) = 12 . . . . . . ( 1 ) also , f + ( f ∩ e ) = 7 ; e + ( f ∩ e ) = 8 . by adding , f + e + 2 ( f ∩ e ) = 15 - - - - - - - - - - ( 2 ) by subtracting ( 1 ) from ( 2 ) , we get ( f ∩ e ) = 3 . ∴ 3 of them read both french and english . answer : b
Answer: B