Problem: 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 ?
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
annotated_formula: subtract(add(8, 7), subtract(15, 3))