$($a$)$ Describe the concept of multi$-$valued dependency and describe how this concept relates to $4NF.$

marks$)$

$($b$)$ The relation shown in Figure $1\mathrm{.}1$ lists the course taught by teachers and hired date. On the other hand, text used for each course is also shown in Figure $1\mathrm{.}1.$

$\backslash$table$[[$Course$,$Teacher,Hired Date,Text,Copyright$],[$BIT$340,$Moore,$1992,340$ Coursepack,$2007],[$BIT$340,$Moore,$1992,$Access,$2007],[$BIT$340,$Ravishankar,$1986,340$ Coursepack,$2007],[$BIT$340,$Ravishankar,$1986,$Access,$2007],[$BIT$301,$Moore,$1992,301$ Coursepack,$2007],[$BIT$301,$Moore,$1992,$Excel,$2007],[$BIT$301,$Moore,$1992,$being digital,$2005],[$BIT$301,$Walls,$1993,301$ Coursepack,$2007],[$BIT$301,$Walls,$1993,$Excel,$2007],[$BIT$301,$Walls,$1993,$being digital,$2005]]$

Figure $1\mathrm{.}1$ CourseTeach Relation

$($i$)$ What is the normal form relation in Figure $1\mathrm{.}1.?$ Justify your answer. $(8$ marks$)$

$($ii$)$ Normalize the table in Figure $1\mathrm{.}1$ to $4$NF and show the steps for each normalization.

$(12$ marks$)$