I'm a newbie to probability theory and am currently working through Chapter 1 of Jaynes' "Probability Theory, The Logic of Science". In it, he introduces the Boolean algebra and a number of identities associated with it, specifically idempotence, commutativity, associativity, distributivity, and duality. However, in this list there seems to be no mention of the following
$\overline{\overline{X}} = X$
i.e. the negation of the negation of the proposition has the same truth value as the proposition and
$X + XY = X$
My question is: why are the two propositional statements above not considered to be "identities" of Boolean algebra? And more generally, what then is the requirement for a propositional statement to be an identity in Boolean algebra?
