Suppose that the universal set is U={1,2,3,4,5,6,7,8,9,10}U={1,2,3,4,5,6,7,8,9,10}. Express each of the following subsets with bit strings (of length 10) where the ith bit (from left to right) is 1 if i is in the subset and zero otherwise.   (a) {3,4,5}{3,4,5}    (b) {1,3,6,10}{1,3,6,10}  (c) {2,3,4,7,8,9}{2,3,4,7,8,9}    (d) {1,2,4,8,10}{1,2,4,8,10}    (e) {3}{3}    (f) {4,5,7,9}{4,5,7,9}

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Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.