7.1 Conditions and conditionals 249
Conditions are familiar in everyday life. Think
about the expression ‘conditions of sale’
which apply when you buy something. You
buy a DVD, for example, on condition that
you don’t make copies of it and sell them on
to other people. The booking conditions on an
airline ticket may allow a refund if you cancel
up to a month before the flight, but not if you
leave it any later. Another familiar example
can be found in the entry requirements –
another word for conditions – that colleges or
universities set for admission. But although
the concept is so familiar, and the word
commonplace in our language, conditions can
cause problems if they are not fully
understood or made clear.
Let’s say you have been offered a place in a
college of choice if you score 70 in the
entrance exam. In other words scoring 70 is a
condition of entry to the college. This might
sound quite plain and straightforward. But it
can be thoroughly ambiguous. For there are
three ways of interpreting a condition of
entry; and how you interpret it can make a lot
of difference to the consequences.
Necessary and sufficient conditions
Conditions fall into two categories according
to whether they are necessary or sufficient.
Scoring 70, for example, could be a necessary
condition, in which case you will not get into
the college if you score 69 or less. But if it is a
necessary condition only, then a score of 70
may not, on its own, be enough to secure you
a place. The exam may be followed by an
interview to choose the best students from all
those who scored 70 or more. This practice is
very common in circumstances where there is
a lot of competition for a limited number of
7.1
Unit 7 Critical reasoning: Advanced Level
Conditions and conditionals
places. Under such a condition, therefore, a
score of 70 would be necessary, but not
sufficient – which could be quite a shock if you
scored 80 and still got turned down!
Alternatively, scoring 70 may be a sufficient
condition. If it is truly sufficient, and you do
score 70, you are accepted, and that is the end of
it. There are no other hurdles to clear. But when
you say something is a sufficient condition, that
doesn’t mean it is also a necessary one. For
example, there may be a second chance for
anyone who scored, say, 60 or more to be
interviewed, and to gain a place that way, so
that as well as those who automatically qualify
by exam there are others who may qualify by
interview. This, too, is a common practice, in
circumstances where there are more places than
there are strong applicants who are likely to
meet the qualifying condition.
There is, of course, a third way of applying
the condition, and that is to make it necessary
and sufficient at the same time. This would
mean that you get in if you score 70 or more
and don’t get in if you score 69 or less. This is
not such a common practice in a context like
entry requirements, for the very good reason
that it would allow no flexibility. If the entry
conditions were both necessary and sufficient,
a department could end up with fewer
students than it would like to have, or with
more than it can cater for.Flow diagrams
One useful way to present this kind of data is in
a flow diagram, or flow chart. From the
following diagram you can read off the
information that a score of 70 is a sufficient
condition for an offer, because a Yes response
leads straight to an offer. But it is not a