$2.$ Consider the following relation:

Articles $($ID$,$ title, journal, issue, year, startpage, endpage, TR$-$ID$)$

It contains information on articles published in scientific journals. Each article has a unique ID$,$ a title, and information on where to find it $($name of journal, what issue, and on which pages$).$ Also, if results of an article previously appeared in a "technical report" $($TR$),$ the ID of this technical report can be specified. We have the following information on the attributes:

$-$ For each journal, an issue with a given number is published in a single year.

$-$ The endpage of an article is never smaller than the startpage.

$-$ There is never $($part of$)$ more than one article on a single page.

$\backslash$begin$\{$tabular$\}\{|$l$|$l$|$l$|$l$|$l$|$l$|$l$|$l$|\}$

$\backslash$hline I & Title & Journal & Issue & Year & StartPage & EndPage & TR$-$ID $\backslash \backslash$

$\backslash$hline $42$ & TCP Networks & JNN & $51$ & $2004$ & $121$ & $138$ & $87\backslash \backslash$

$\backslash$hline $33$ & Sensor Nodes & JNN & $41$ & $2001$ & $69$ & $85$ & $62\backslash \backslash$

$\backslash$hline $33$ & Sensor Nodes & JNN & $41$ & $2001$ & $69$ & $85$ & $56\backslash \backslash$

$\backslash$hline $39$ & Deep Learning & SICOMP & $31$ & $2001$ & $111$ & $133$ & $47\backslash \backslash$

$\backslash$hline $57$ & NP Problems & JA & $51$ & $2008$ & $1$ & $3$ & $99\backslash \backslash$

$\backslash$hline $77$ & ANT Disease & SICOMP & $51$ & $2008$ & $1$ & $6$ & $98\backslash \backslash$

$\backslash$hline $78$ & ANT Disease & NAT & $2222$ & $2008$ & $22$ & $22$ & $98\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$ a$.$ Based on the above, indicate which of the following sets of attributes is a candidate key for Articles. $1.\backslash \{$ID$\backslash \}$; $2.\backslash \{$ID$,$TR$-$ID$\backslash \}$; $3.\backslash \{$ID$,$title,TR$-$ID $\backslash \}$

$[2$ mark$]$

b$.$ Based on the above, indicate for each of the following potential functional dependencies, whether it is indeed an FD or not.

i$.$ ID $->$ title;

ii$.$ startpage $->$ endpage;

iii. journal, issue $->$ year

iv$.$ title $->$ ID

v$.$ ID $->$ startpage, endpage, journal, issue

vi$.$ TR$-$ID $->$ ID

$[6$ marks$]$

c$.$ Explain whether or not the Articles relation is in $1$ NF $.$

$[2$ mark$]$

d$.$ Perform normalization into $3$ NF and state the resulting relations.

$[5$ marks$]$