Consider the following identification number scheme: if w $=(2,4,5,7,8),$ and n$=9.$that above information mean that

$($a$1,$ a$2,$ a$3,$ a$4,$ a$5),$ with each ai an integer with $0<=$ ai $<=7,$ is valid if and only if $.$

Show that this scheme detects transposition error in the third, and fourth digit. Give an example

of a valid codeword and an error in the third digit of the codeword that is not detected