$43.$ Express each of these system specifications using predi$-$cates, quantifiers, and logical connectives.

a$)$ At least one mail message, among the nonempty set

of messages, can be saved if there is a disk with more than $10$ kilobytes of free space.

b$)$ Whenever there is an active alert, all queued messages are transmitted.

c$)$ The diagnostic monitor tracks the status of all systems except the main console.

d$)$ Each participant on the conference call whom the host of the call did not put on a special list was billed.