Question $3$: $[4$ marks$]$

Express each of these system specifications using predicates, quantifiers, and

logical connectives.

a$)$ Every user has access to an electronic mailbox.

b$)$ The system mailbox can be accessed by everyone in the group if the file system

is locked.

c$)$ The firewall is in a diagnostic state only if the proxy server is in a diagnostic

state.

d$)$ At least one router is functioning normally if the throughput is between $100$

kbps and $500kbps$ and the proxy server is not in diagnostic mode.