7.1 Conditions and conditionals 253
B Possession of an ADQ and a clean
licence are sufficient for approval.
C Being 25 or over is neither a
necessary nor a sufficient condition
for approval.
D For Jason, who is 23, passing an ADQ
is a necessary but insufficient
condition for approval.
E Being under 21 is a sufficient
condition for refusal.3 (Harder task)
It is just as well, from an evolutionary
standpoint, that water freezes with its
molecules bonding to form a very
open lattice. This unusual structure is
such that the density of water ice is
less than that of liquid water, which is
why ice floats unlike other solids with
tighter structures such as iron. (An iron
bar placed in molten iron will sink.)
Where and when the oceans freeze, ice
forms a layer of insulation on the
surface which holds in the heat of the
liquid below. Without this protection
the seas would freeze solid, from the
bottom up; and life as we know it,
which began in water, would not exist.
Explain and assess the reasoning in the
above argument. In your analysis state
whether the unusual structure of water is
presented as:• a sufficient condition for life as we know it
• a necessary but insufficient condition
for life as we know it
• both a necessary and sufficient
condition for life as we know it
• neither a necessary nor sufficient
condition for life as we know it.Answers and comments are on page 339.1 A tutor made the following prediction to a
group of students: ‘If you have not read the
coursebook, you won’t pass the exam.’
a Explain this prediction in terms of
necessary and sufficient conditions.
b Which one of the following has to be true
if the tutor’s prediction was correct – and
why do the others not have to be true?
A All those who read the book passed
the exam.
B All those who had not read the book
failed the exam.
C The same number of students read
the book as passed the exam.
D Only those who passed the exam had
read the book.
E None of those who failed the exam
had read the book.
OCR
2 A car insurance company has special
terms for young drivers. If the driver is 25
or over and has a clean licence (i.e. no
driving convictions), then the application
is approved. If the driver has a clean
licence and is under 25 but is 21 or over,
the application is approved only if he or
she has an Advanced Driving Qualification
(ADQ). Applications from drivers under
25 with no ADQ are refused. Drivers are
also refused if they are under 21 (with or
without an ADQ). So are any drivers who do
not have a clean licence.
a Draw a flow diagram which represents
the information in the above text. (It is
advisable to start with: ‘Clean licence –
Yes or No?’
b Use your diagram, and/or the text, to say
whether each of the following statements
is correct or incorrect – and why:A Being 21 or over is a necessary
condition for approval.End-of-chapter assignments