diff --git a/work_files/verum-nimply_logic.md b/work_files/verum-nimply_logic.md index b3f27a9d4..4646945ac 100644 --- a/work_files/verum-nimply_logic.md +++ b/work_files/verum-nimply_logic.md @@ -34,14 +34,14 @@ This document will use the convention where the Collector is placed on the lefth ### Falsum ⊥ = (⊤ ↛ ⊤) +### NOT p += (⊤ ↛ p) + ### Buffer p = (p ↛ ⊥) = NOT (NOT p) = (⊤ ↛ (⊤ ↛ p)) -### NOT p -= (⊤ ↛ p) - ### p AND q = (p ↛ (NOT q)) = (p ↛ (⊤ ↛ q)) @@ -65,3 +65,23 @@ Method 2: = (⊤ ↛ ((⊤ ↛ p) ↛ (⊤ ↛ (⊤ ↛ q)))) = (⊤ ↛ ((⊤ ↛ p) ↛ q)) Note: For the most cases, an OR gate can be substituted using merging wires and buffers. + +### p NOR q += NOT (p OR q) += NOT (NOT(p) AND NOT(q)) += NOT(p) AND NOT(q) += ((⊤ ↛ p) ↛ (⊤ ↛ (⊤ ↛ q))) += ((⊤ ↛ p) ↛ q) + +### p XOR q += (p OR q) AND NOT(p AND q) += (p OR q) AND (p NAND q) += (⊤ ↛ ((⊤ ↛ p) ↛ q)) AND (⊤ ↛ (p ↛ (⊤ ↛ q))) += ((⊤ ↛ ((⊤ ↛ p) ↛ q)) ↛ (⊤ ↛ (⊤ ↛ (p ↛ (⊤ ↛ q))))) += ((⊤ ↛ ((⊤ ↛ p) ↛ q)) ↛ (p ↛ (⊤ ↛ q))) + + + + + +