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redundant
in
r
if and only if it's either
partly
redundant or
fully
redundant. The paper shows that (a) such a tuple

exists and is partly redundant if and only if
R
isn't in BCNF (i.e., if and only if
R
is FD redundant─see Chapter 13);

(b) such a tuple exists and is fully redundant if and only if a tuple forcing JD holds in
R
(i.e., if and only if
R
is JD

redundant─again, see Chapter 13). Note, therefore, that “fully redundant” is not a special case of “partly

redundant”; in fact, a tuple can be partly redundant without being fully so or the other way around. Finally, tuple
t
is

essential
in
r
if and only if it's not redundant in
r
. If
R
is in ETNF, then every relation
r
that's a legitimate value for

R
is such that every tuple is essential in
r
.
Note:
Our choice of the term
essential
for use in this context was

influenced by Codd's notion of essentiality, introduced in E. F. Codd and C. J. Date: "Interactive Support for

Nonprogrammers: The Relational and Network Approaches," in Randall J. Rustin (ed.), Proc. ACM SIGMOD

Workshop on Data Description, Access, and Control─Data Models: Data-Structure-Set
versus
Relational (Ann

Arbor, Michigan, May 1st-3rd, 1974).
3
Briefly, to say some data construct is essential in Codd's sense is to say its

loss would cause a loss of information. As already indicated, every tuple in every relation that's a possible value for

an ETNF relvar is essential in this sense.

3
Republished in C. J. Date,
Relational Database: Selected Writings
(Addison-Wesley, 1986).