Required to model a system using mathematical logic constructs to
describe how the system works. You should fully describe the constructs you are using, including
any assumptions, and justify your modelling assertions.
Learning Outcomes to be assessed
• Apply appropriate mathematical concepts and operations to solve problems.
• Evaluate possible solutions to problems and defend the chosen solutions.
Detail of the task
Part A:
As the Internet of Things (IoT) becomes more prevalent with the integration of more smart
devices onto networks, software will be needed to manage and control these devices. At the
software control level, the operational rules required will consist of logical statements. For
example, consider a simple smart Vending Machine, dispensing just one product. The machine
will accept coins (or maybe credit cards, mobile phone payments, etc.) and allow a product to
be dispensed only in circumstances where the correct amount for the product has been
received, by the machine, and the product has been requested
1. If P is the assertion that the correct money has been received, Q is the assertion that the
product has been requested and R is the assertion that the product will be dispensed,
then represent these facts in a statement using logical propositions and connectives.
2. Using the assertions P and Q, from A1, and logical connectives, represent the statement:
The correct money has been received or the product has been selected and it is not the
case that both the product has not been selected and the correct money has been
inserted, then simplify the resulting expression using laws of logical equivalence.
3. If the correct money has been received and the product has been selected then the product
will be dispensed (as represented in A1). Again, representing P as the correct money has
been inserted with Q the assertion that the product has been requested and R the assertion
that the product will be dispensed, represent the converse, inverse and contrapositive of
this assertion and comment on the truth-value of these, if the assertion (from A1) is known
to be true.
4. Represent the following statements in logic sentences:
i. If the correct money is inserted then if the product is selected then the
product will be dispensed.
ii. If the correct money is inserted and the product is not dispensed then
the product has not been selected.
iii. If the product is not dispensed then the correct money has not been inserted
orthe product has not been selected.
iv. If it is not the case that the correct money has not been inserted or the
product has not been selected then the product will be dispensed.
5. Construct a truth table for the logic sentences in question A4 and comment on
the equivalence or otherwise of the statements.
Part B:
Vending machines are, of course, nowmuch more sophisticated than the one described in section
A, above. There can be multiple itemsto choose from; stock can be monitored, for freshness and
level, and the machine it self can alert to signal a restock, coins can be checked for validity;
change given; personal accounts maintained; customer detection with a personal message, etc.
Additionally, to cope with his added complexity, predicates need to be used instead of the
propositions used in section A. For example, as there are multiple items that can be dispensed, a
predicate dispense(x) could be used to mean product x is dispensed by the machine (e.g.
dispense(StarBurst_tube))
Describe, in your own words and with diagrams if necessary, a description for the operation of
Vending Machine. Your machine should be ‘state of the art’ and dispense a number of different
products with varying prices, accepting different coins/notes.
List the different states that the vending machine, you have described, can be in and discuss the
conditions that dictate the entering and leaving of these states.
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