Theory question 108
Sets(a) A = {1,2,5,7} and B = {1,3,6,7} are subsets of the universal set U = {1,2,3,....., 10}. Find: (i) A' (ii) (A∩B)'; (iii) (A∪B)', (iv) the subsets of B each of which has three elements.
(b) Write down the 15th term of the sequence 2/(1 × 3), 3/(2 × 4), 4/(3 × 5), 5/(4 × 6), ..........
(c) An Arithmatic Progression (A.P) has 3 as its first term and 4 as the common difference. (i) Write an expression, in its simplest form for the nth term. (ii) find the least term of the AP that is greater than 100.
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(a)(i) A' = {3, 4, 6, 8, 9, 10}.
(ii) A∩B = {1, 7}, so (A∩B)' = {2, 3, 4, 5, 6, 8, 9, 10}.
(iii) A∪B = {1, 2, 3, 5, 6, 7}, so (A∪B)' = {4, 8, 9, 10}.
(iv) {1, 3, 6}, {1, 3, 7}, {1, 6, 7}, {3, 6, 7}.
(b) Tn = (n + 1)/[n(n + 2)], so T15 = 16/(15 × 17) = 16/255.
(c)(i) Tn = 3 + 4(n − 1) = 4n − 1.
(ii) 4n − 1 > 100 gives n > 25.25, so n = 26 and the term is 103.
Spot the pattern in the numerator and each factor of the denominator separately.