(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 subjects? (iii) What is (n(P cup G))?
(b) If (p = frac{2u}{1 – u}) and (q = frac{1 + u}{1 – u}) ; express (frac{p + q}{p – q}) in terms of u.
Explanation
(a) (i)
(ii) (32 – x + x + 28 – x + 12 = 45)
(72 – x = 45)
(x = 72 – 45 = 27)
27 students offered both Physics and Government.
(iii) (n(P cup G) = 45 – 12 = 33)
(b) (p = frac{2u}{1 – u} ; q = frac{1 + u}{1 – u})
(frac{p + q}{p – q})
(p + q = frac{2u}{1 – u} + frac{1 + u}{1 – u})
= (frac{2u + 1 + u}{1 – u})
= (3u + 1}{1 – u})
(p – q = frac{2u – 1 – u}{1 – u})
= (frac{u – 1}{1 – u})
= (frac{-(1 – u)}{1 – u})
= (-1)
(frac{p + q}{p – q} = frac{frac{3u + 1}{1 – u}}{-1})
= (frac{-(3u + 1)}{1 – u})
= (frac{-(3u + 1)}{-(u – 1)})
= (frac{3u + 1}{u – 1})