Discrete Structures Connectives (Equivalences Focus)

Implication, Biconditional, XOR, NAND, NOR focus on their equivalences only using negation, conjunction, and/or disjunction.

Implication (→)

¬P Q
“not P and Q”

Biconditional (↔)

(P ∧ Q)  ∨ (¬P ∨ ¬Q)
“(P and Q) or (not P and not Q)”

XOR (⊕)

(P∨Q)∧¬(P∧Q)
“(P or Q) and not (P and Q)”

NAND (↑)

¬(P∧Q)
“Not (P and Q)”

NOR (↓)

¬(P∨Q)
“Not (P or Q)”