Question

Suppose that the universal set is\(U = \{ 1,2,3,4,5,6,7,8,9,10\} .\)Express each of these sets with bit strings where the\(i\)th 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) \(\{ 2,3,4,7,8,9\} \)

Short answer

Hence, we conclude that

a) \(0011100000\)

b) \(1010010001\)

c) \(0111001110\)

Step-by-step solution

Step 1

Given: \(U = \{ 1,2,3,4,5,6,7,8,9,10\} .\)

If the i th bit in the string is a 1, then i is in the set.

If the i th bit in the string is a 0, then i is NOT in the set.

Step 2

(a) Given: \(\{ 3,4,5\} \)

The set contains\(3,4,\)and\(5.\)

The string corresponding to this set then contains\(10\)digits of which the\(3\)rd,\(4\)th and\(5\)th digit is one, while all other digits are\(0\)’s.

\(0011100000\)

Step 3

(b) Given: \(\{ 1,3,6,10\} \)

The set contains, \(1,3,6,\)and\(10.\)

The string corresponding to this set then contains\(10\)digits of which the\(1\)st,\(3\)rd,\(6\)th and\(10\)th digit is\(1\), while all other digits are\(0\)’s.

\(1010010001\)

Step 4

(C) Given: \(\{ 2,3,4,7,8,9\} \)

The set contains\(2,3,4,7,8,\)and\(9\).

The string corresponding to this set then contains\(10\)digits of which the\(2nd,3rd,4th,7th,8th,\)and\(9th\)digit is\(1\), while all other digits are\(0\)’s.

\(0111001110\)