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5. Suppose that the universal set is U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Express each of thesesets with bit strings where the ith bit in the string is 1 if i is in the set and 0 otherwise.a) {3, 4, 5} b) {1, 3, 6, 10} c) {2, 3, 4, 7, 8, 9}

Question

  1. Suppose that the universal set is U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Express each of thesesets with bit strings where the ith bit in the string is 1 if i is in the set and 0 otherwise.a) {3, 4, 5} b) {1, 3, 6, 10} c) {2, 3, 4, 7, 8, 9}
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Solution

a) {3, 4, 5} can be represented as 0011100000. Here, the 3rd, 4th, and 5th bits are 1 because 3, 4, and 5 are in the set.

b) {1, 3, 6, 10} can be represented as 1010010001. Here, the 1st, 3rd, 6th, and 10th bits are 1 because 1, 3, 6, and 10 are in the set.

c) {2, 3, 4, 7, 8, 9} can be represented as 0111001110. Here, the 2nd, 3rd, 4th, 7th, 8th, and 9th bits are 1 because 2, 3, 4, 7, 8, and 9 are in the set.

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