True or False $(10$ points, $1$ points for each$)$

$()(1)$ One important advantage of database system is elimination of data redundancy.

$()(2)$ A key is a super key but not vice versa.

$()(3)$ A rule that should not be violated by a database user is called a constraint.

$()(4)$ Unordered records allow for faster access to data.

$()(5)$ Delete operation only mark data as invalid.

$()(6)$ Attributes of an entity are properties of that entity.

$()(7)$ An index file usually occupies considerably less disk space than the data file because its

entries are much smaller.

$()(8)$ The transitive rule for FD$\text{'}$s states: if $(xy)$ then $xzyz.$