Theory question 104
Sets(a) In a class of 45 students, 32 offered Physics (P), 28 offered Government (G) and 12 did not offer any of the two subjects. (i) Draw the Venn diagram to represent the information. (ii) How many students offered both Physics and Government? (iii) What is n(P∪G)?
(b) If p = 2u/(1 − u) and q = (1 + u)/(1 − u), express (p + q)/(p − q) in terms of u.
Show the model answer
Model answer
(a)(i) Two overlapping circles P and G inside U (45): P only = 32 − x, both = x, G only = 28 − x, outside = 12.
(ii) (32 − x) + x + (28 − x) + 12 = 45, so 72 − x = 45 and x = 27.
(iii) n(P∪G) = 45 − 12 = 33.
(b) p + q = (2u + 1 + u)/(1 − u) = (3u + 1)/(1 − u); p − q = (2u − 1 − u)/(1 − u) = (u − 1)/(1 − u).
(p + q)/(p − q) = (3u + 1)/(u − 1).
Explanation
Put x in the overlap and add all regions to the total.