Question

i need to know how to do this based on shown work for future reference.

4) A group of 1487 students were surveyed about the courses they were taking at their college with the following results: 704 students said they were taking Psychology. 761 students said they were taking Science. 834 students said they were taking Math. 803 students said they were taking Dance. 463 students said they were taking Dance and Math. 541 students said they were taking Science and Math. 390 students said they were taking Psychology and Science. 420 students said they were taking Psychology and Dance. 204 students said they were taking Psychology, Dance, and Math. 315 students said they were taking Science, Dance, and Math. 206 students said they were taking Psychology, Science, and Dance. 297 students said they were taking Psychology, Science, and Math. 167 students said they were taking all four courses. Fill in the following Venn Diagram with the cardinality of each region. So that you do not need to draw the 4 set Venn Diagram, here is a printable version: Printable 4 Set Venn Diagram Psychology Science III. VII. VIII. VI. IX. XII. XIII Dance Math XIV.

Answer 1

Solution Psychology science / I 111X rance Math • VI represents the region common to all the four fields and since, 167 said they were taking all four Courses ir sses . VI = 167. • 297 Students said they were taking leychology, Science and Math. So, VI + VII = 297 o's VII = 294-167 = 130 .

206 students said they were taking Psychology, science and Dance. These three fields together are represented by V o. V + VI = 206 → V = 206 - 167 = 39 ented by V+ VI 315 students said they were taking Science, dance and Math. In Venn Yiagram, The common region to these three fields is marked by 11 + So, VI + X = 315 → X = 315- 167 → X = 148 • 204 students were taking Psychology, Dance & Math So, 1x + VI = 204 IX = 204-167 → IX = 37 • 420 students were taking Bsychology and Dance IV + y + V1 + 1x = 420 + 1 V - 420-37-167–39 + IV = 177

• 390 students were taking psychology and Science. So, II + V + Vil + VI = 390 → II = 390 – 167 – 130- 39 + TI = 54 541 students were taking Science and Math So, VI + VII + VIII + X = 1541 * VIII= 541–148–130-167 7 Vill = 196

Vi= 167 II = 54 IX = 37 V11 = 130 IV = 177 X = 148 VIII = 196 V = 39 463 students were taking yance and Math VIP 1 X + X ]] + x = 463 80, Vit 800 - XII = 463-148-37-167 * XII - (. 803 students were taking Tance So, XI+ Xll + 1 X+VI+ IV +V + x = 803 → XI = 803 – 111- 37–167-177–39–148 * XI = 124 - 834 were taking mattis 1 So, X111 + X11 + IX + Students taking Science = 834 And Matty + XIII = 834–541– 37- 111 + XILC - 145. • 761 students were taking science IIL + x + Vill + Students with Science – 76) . Psychology 4 11 [ = 761-148–196 – 390 = .7

Jou students said they were taking Psychology - 1 + 1 + 1X + Students with Psychology & _74 - Science = 1 = 704 - 390 -37-177 * 1 - 100 We Have I= loo V = 39 12 = 54 1X = 37. I 1= 167 III = 27 X = 148 Vll = 130 XI = 124 1y = 177 VIII = 196 $1] = 111 X ]= 145 Question: i students taking science but not dance = 1] + 11 L + V 1L + VIII = 54+27 +130 +196 =407 i) How many students are taking none of the courses? Answer: 1487- ( + 1] +----+ XIII) = = 1487-1455 = 32

100 e and Students Not Taking Yance & Math of Taking Yance & Rychology = (1 + II + 111) + (: 420) V = 100+54 +27 +420 = 6ol students are taking lsychology, Science and Maths but not Yance = 1 + 11 + ]]] + VII + Vill+ X111 = 100 +54 27+ 130 + 1967 145 -652 e) Students taking (Roychology & Math) or (Science of Dance) = (1x + VI + VII) + (v + x) Ý VI has = 377 167+ 130 + 39 + 148 =521 accounted f) Students taking Psychology & Math but not fance = VII = 130 9 students not taking Science, dance or Math already been . Hol

h) Students taking Psychology, Science or Mala = Total – XI = 1455-124 = 1331 D. students not taking Science = 1455,- Süence = 1455-761= (Total) 694