A survey was conducted to determine the popularity of 3 foods among students. The data collected from 75 students are summarized as below 48 like Pizza 45 like Hoagies 58 like tacos 28 like pizza and hoagies 37 like hoagies and tacos 40 like pizza and tacos 25 like all three food

Answer:The number of students who like none or only one of the foods is 20.Step-by-step explanation:Consider the provided information.First draw the Venn diagram as shown below:25 like all three food and 40 like pizza and tacos .40-25=15 likes only pizza and tacos.25 like all three food and 37 like hoagies and tacos 37-25=12 likes only hoagies and tacos 25 like all three food and 28 like pizza and hoagies 28-25 = 3 like only pizza and hoagies .Let P represents Pizza, H represents Hoagies and T represents Tacos.Only Pizza = P - (only P and H + only P and T + All 3 foods) Only Pizza = 48 - (3+ 15 + 25) = 5 Only Hoagies = H - (only P and H +only H and T - All 3 foods) Only Hoagies = 45 - (3 + 12 + 25) = 5Only Tacos = T - (only P and T + only H and T - All 3 food) Only Tacos = 58 - (15 + 12 + 25) = 6Total number of students are 75.Total number of student who don't like any of the food is:Total=P+H+T−(sum of 2 group overlaps)+(all three)+Neither75=48+45+58−(28+37+40)+25+Neither75=176−(105)+NeitherNeither = 4The number of students who like none or only one of the foods = 4 + (5 + 5 + 6) = 20.Hence, the required answer is 20.