Express each of these system specifications using predicates, quantifiers, and logical connectives, if necessary. a. At least one console must be accessible during every fault condition.
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.
c. For every security breach there is at least one mecha- nism that can detect that breach if and only if there is a process that has not been compromised.
d. There are at least two paths connecting every two dis- tinct endpoints on the network.
e. No one knows the password of every user on the sys- tem except for the system administrator, who knows all passwords.

Step-by-step explanation:

1. we have to write the system specifications as:

A(x,y) give us the meaning that the consule x can be accessed when y is in a faulty condition

∀y∃A(x,y)

2. B(x,y) shows that users email has sent a message, y. Which is in the archive. C(x) shows the email address of user x is retrievable

∀x∃y[B(x,y)→c(x)]

3. D(x,y) shows that x can detect breach y'' and we have E(z) that tells us there is a compromise of z

∀y∃xD(x,y)↔ ∃zE(z)

4. F(x,y,z)

Y and z are distinct point ends which x connects

We have,

∀y∀z∃x∃a[x ≠a →F(x,y,z)^F(a,y,z)

5. G(x,y)

X knowst the password of y' and H(x) means that we have x to be a system administrator

∀x[H(x)→∀yG(x,y)] ∃x[H(x)^∀yG(x,y)]

b

step-by-step explanation:

a difference is the result of subtraction. while each of these expressions has subtraction in it, a difference will be the result when subtraction is the last operation applied in the order of operations for the expression. this means subtraction must be outside of the parenthesis. only b has this.