Hand-in @ lecture #5

Author

Jonas Smedegaard

Published

31 March 2026

1.3.12

Let \(I(x)\) be x has an Internet connection, and
let \(C(x, y)\) be x and y have chatted over the Internet, where
\(S\) is all students in this class and
\(x \in S\) and
\(y \in S\)

a)

The expression Jerry does not have an Internet connection. can be expressed in propositional logic as \(\lnot I(a)\).

b)

The expression Rachel has not chatted over the Internet with Chelsea. can be expressed in propositional logic as \(\lnot C(b, c)\).

c)

The expression Jan and Sharon have never chatted over the Internet. can be expressed in propositional logic as \(\lnot C(d, e)\).

d)

The expression No one in the class has chatted with Bob. can be expressed in propositional logic as \(\exists ! x C(x, f)\).

1.3.18

a)

At least one console must be accessible during every fault condition.

Let \(A(x)\) be console is accessible for any \(x in\) consoles, and
\(F(x)\) be condition is at fault for any \(x in\) conditions.

\(\forall x\exists y(F(x) \land A(y))\)

b)

The e-mail address of every user can be retrieved whenever the archive contains at least one message sent by every user on the system.

Let \(A(x)\) be address of user can be retrieved for any \(x in\) users, and
\(Z(x)\) be archive contains message for any \(x in\) messages, and
\(O(x, y)\) be message was sent by user for any \(x in\) messages and \(y in\) users, and
\(S(x)\) be user is on the system for any \(x in\) users.

FIXME $x ((Z(S(x))

c)

For every security breach there is at least one mechanism that can detect that breach if and only if there is a process that has not been compromised.

1.3.50

1.3.56