We conclude this chapter with a set of identities pertaining to special cases and compositions of logical operations.
The first two lemmas are immediate consequences of the definitions.
PROOF: By Definition 3.2.1, .
All of the remaining results of this section may be derived in a straightforward manner from Lemmas 3.2.5, 3.1.14, and 2.3.22.
PROOF: Suppose . By Lemma 3.1.14, for all
The proofs the remaining lemmas are sufficiently similar to that of Lemma 3.3.5 that they may be safely omitted.
David Russinoff 2017-08-01