Theory question 106
Sets(a) The subsets A, B and C of a universal set are defined as follows: A = (m,a,p,e) B = (a,e,i,o,u) C = (l,m,n,o,p,q,r,s,t,u)
List the elements of the following sets: (i) A∪B (ii) A∪C (iii) A∪(B∩C)
(b) Out of the 400 students in the final year in a Senior Secondary School, 300 are offering Biology and 190 are offering Chemistry. (i) How many students are offering both Biology and Chemistry, if only 70 students are offering neither Biology nor Chemistry? (ii) How many students are offering at least one of Biology or Chemistry?
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(a)(i) A∪B = {a, e, i, m, o, p, u}
(ii) A∪C = {a, e, l, m, n, o, p, q, r, s, t, u}
(iii) B∩C = {o, u}, so A∪(B∩C) = {a, e, m, o, p, u}
(b) Let x offer both. n(B∪C) = 400 − 70 = 330.
(300 − x) + x + (190 − x) = 330 ⇒ 490 − x = 330 ⇒ x = 160.
(i) 160 students offer both.
(ii) 330 students offer at least one of the two.
Draw a Venn diagram; the 70 outside both circles are taken from the 400 first.