Answer to Question #323484 in Discrete Mathematics for Gillani

Question

What is the 10-bit string for the complement of 10-bit string 1010101010.

Answer 1

The bit strings for two sets are given as:-

$A=0110011100 \text{ which corresponds to set }\text{{}2,3,6,7,8}$

$B=1010101010 \text{ which corresponds to set} 1,3,5,7,9$

Union of two set is-

$A\cup B=1110111110$

which corresponds to {${1,2,3,5,6,7,8,9}$ }

Intersection of two set is -

$A\cap B=0010001000$

which corresponds to {$3,7$ }

Compliments of A and B i.e. $(A\cap B)'$

$1101110111$ which corresponds to the set {$1,2,5,6,8,9$ }