Judgments
Mathematical Techniques for Computer Science.pdf
- Course
- Computer Science
- Institution
- Computer Science
Mathematical Techniques for Computer S
[Show more]
Seller
Follow
Content preview
COMP11120Two hours
Note that the last two pages contain inference reules for natural deduction
UNIVERSITY OF MANCHESTER
SCHOOL OF COMPUTER SCIENCE
Mathematical Techniques for Computer Science
Date: Tuesday 19th January 2016
Time: 14:00 - 16:00
Please answer ALL THREE Questions
Use a SEPARATE answerbook for each SECTION.
This is a CLOSED book examination
The use of electronic calculators is permitted provided they are not programmable and do not store text
[PTO]
, COMP11120
Section A
1. a) Give a situation in which you, as a programmer, might be concerned with a function
being injective. How might you check that your implementation does indeed give
an injective function? (3 marks)
b) Consider the following function:
C C
z z · z.
i) Is this function injective? Justify your answer. (2 marks)
ii) Is this function surjective? Justify your answer. (5 marks)
c) Consider the binary operation on the set {a, b, c} given by the following table.
~ a b c
a a a c
b a b c
c a c c
i) Is the given operation commutative? Give a reason for your answer.
(2 marks)
ii) Is the given operation associative? Give a reason for your answer.
(4 marks)
d) Show that if
f:S T and g: T U
are two bijective functions then so is their composite (4 marks)
g◦ f : S U.
Page 2 of 7
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through EFT, credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying this summary from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller Studyabroad. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy this summary for R137,88. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
79650 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy summaries for 14 years now