Mark each statement True or False. Justify each answer. (a) To prove a universal statement ∀ x, p (x), we let x represent an arbitrary member from the system under consideration and show that p (x) is...

Mark each statement True or False. Justify each answer.

(a) To prove a universal statement ∀ x, p (x), we let x represent an arbitrary member from the system under consideration and show that p (x) is true.

(b) To prove an existential statement ∃ x
 p (x), we must find a particular x in the system for which p (x) is true.

(c) In writing a proof, it is important to include all the logical steps.