IS2150/TEL2810 Introduction to Security
Homework 2
Total Points: 50
1) Exercise on Propositional/Predicate logic [25 Points]
(a) Prove that A
B
⇔
(A
∧￢
B)
∨
(
￢
A
∧
B) (you can use the truth table) (5 points)
(b) Express the following sentences in propositional/ first order logic. Be sure to
define all propositional components (e.g., predicate function, constants, and variables).
i) If it does not
rain we will go to the Steeler’s game. (3 points)
R = it rains
S = go to Steelers game
R → S
ii) If a subject has Secret clearance then he/she is allowed to write to Secret
and Top Secret files (3 points)
SecretSubject(x) = subject x has secret clearance
TopSecretFile(f) = file f is top secret
SecretFile(f) = file f is secret
allowWrite(x, y) = subject x is allowed to write to file y
x
f [ SecretSubject(x)
((SecretFile(f)
TopSecretFile(f))
→
canWrite(x,f) ) ]
iii) A person can approve a check or cash it but cannot do both. (3 points)
canApprove(x, c) = x can approve check c
canCash(x, c) = x can cash check c
x,
c [
(canApprove (x, c)
canCash(x, c))
(canCash(x, c)
canApprove(x, c)) ]
iv) A directory is older than the directories and the files that it contains. (4
points)
isOlder(x, y) = x is older than y
isDirectory(x) = x is a directory
isFile(x) = x is a file
Contains(x, y) = x contains y
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 Spring '09
 joshi
 administrator, Dave, File system permissions, Steelers, security descriptor

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