Question

(1 point) In a survey of 263 college students, it is found that 62 like brussels sprouts, 100 like broccoli, 59 like cauliflower, 30 like both Brussels sprouts and broccoli, 22 like both Brussels sprouts and cauliflower, 20 like both broccoli and cauliflower, and 12 of the students like all three vegetables. a) How many of the 263 college students do not like any of these three vegetables? b) c) d) How many like broccoli only? How many like broccoli AND cauliflower but not Brussels sprouts? How many like neither Brussels sprouts nor cauliflower?

Answer 1

N(BS) = 62, N(BC) = 100 N(CF) = 59 N(BS intersection BC) = 30 N(BS intersection CF) = 22 N(BC intersection CF) = 20 N(BC intersection BS intersection CF) = 12 BS: Brussels sprouts BC: Broccoli CF: Cauliflower Total no. of students = Because N(BC Union BS Union CF) = N(BC) + N(BS) + N(CF) - N(BC intersection BS) - N(BS intersection CF) - N(BC intersection CF) + N(BC intersection BS intersection CF) = 62 + 100 + 59 - 30 - 22 - 20 + 12 = 161 Therefore no. of Students who do not like any of these three vegetables = total No. of students - No. of students Who like either BC or BS or CF = 263 - 161 = 102 \r\n No. of students Who like broccoli only = N(BS) - N(BS intersection BC) -N(BS intersection CF) + N(BS intersection BC intersection CF) = 62 - 30 - 22 + 12 = 22