$6.$ Please draw the relationship diagram for P$,$ NP$,$ NP$-$Complete and NP$-$Hard problems. $(5$ points$)$

$7.$ The following hamming code word was received. Use it to answer questions $(1)-(5).(27$ points$)$

$0000110$

$(1)$ What position number is generated to determine if an error has ocurred in transmission? $(10$ points$)$

$(2)$Did an error occur? $(2$ points$)$

$[]$:

$(3)$ What was the transmitted code word? $($correct code$)(5$ points$)$

$(4)$ What was the transmitted message? $($correct message$)(5$ points$)$

$(5)$ If the message was binary, what was the decimal value of the correct message? $(5$ points$)$