Logic Boolean Computation not a and a not (a and b) not a and b not a AND 1, 0, 0, 0 [And] Boolean Computation Boolean Computation not b and a not b not (a and b) and (a or b) not (a and b) OR 1, 1, 1, 0 (Or) Logic & Boolean Algebra Boolean Computation a and b a and b or not (a or b) b not a or b NOT 0, 1 (not] Use Logical Operators Boolean a not b or a a or b not a or a Conjugate Transpose Conjugate Matrix Boolean algebra Canonical Boolean algebras not a and a not a and not b not a and b not a AND 1, 0, 0, 0 [and] Boolean Function Boolean Function not b and a not b !(!a and !b) and !(a and b) not (a and b) NOT 0, 1 (not) a and b !(!a and b) and !(!b and a) b not (not b and a) a not (not a) and b not (not a and not b) not (not a and a) not (not a or a) not (a or b) not (not b or a) not a OR 1, 1, 1, 0 (or) not (not a or b) not b !(!a or b) or !(!b or a) not a or not b NOT 0, 1 (not) not (not a or not b) !(!a or !b) or !(a or b) b not a or b a not b or a a or b !a or a not (a implies a) not (not a implies b) not (b implies a) not a Implies 1, 1, 0, 1 (Implies] not (a implies b) not b (a => b) => ¬(b=>a) a implies not b NOT 0, 1 (not) not (a implies not b) !((a => b) => !(b => a)) b a implies b a b implies a not a implies b a implies a
a xor a (a implies b) xor b ((a => b) => b) xor a (a implies a) xor a XOR 0, 1, 1, 0 (Xor) ((a => b) => b) xor a (a implies a) xor b a xor b (a implies b) xor a Implies 1, 1, 0, 1 [Implies] (((a => b) => b) xor a) xor ... ((a => a) xor a) xor b b a implies b a b implies a (b implies a) implies b a implies a a ∘ a a ∘ (a ◌̅ b) a ∘ b a ∘ (a ◌̅ a) Complement Set [f2] 0, 1, 0, 0 (∘) b ∘ a b ∘ (a ◌̅ a) a ∘ b ◌̅ (b ◌̅ a) a ∘ b ◌̅ b OverBar [f13] 1, 0, 1, 1 (◌̅) (a ∘ b) ∘ b (a ∘ b) ∘ (b ∘ a) b a ◌̅ b Overline Composition a b ◌̅ a a ◌̅ (a ◌̅ b) a ◌̅ a Composition (combinatorics) Composition of relations ((a ⊼ a) ⊼ a) ⊼ ((a ⊼ a) ⊼ a... ((a ⊼ a) ⊼ (b ⊼ b)) ⊼ ((a ⊼ ... ((a ⊼ a) ⊼ a) ⊼ ((a ⊼ a) ⊼ b... a nand a 0, 1, 1, 1 (Nand) NAND ((a ⊼ a) ⊼ a) ⊼ ((a ⊼ b) ⊼ a... b ⊼ b ((a ⊼ a) ⊼ b) ⊼ ((a ⊼ b) ⊼ a... a nand b Wolfram Axiom (a nand b) nand (a nand b) ((a ⊼ a) ⊼ (b ⊼ b)) ⊼ (a ⊼ b... b (a nand b) nand a a (a nand a) nand b (a nand a) nand (b nand b) (a nand a) nand a (a nor a) nor a a nor b (a nor b) nor a a nor a 0, 0, 0, 1 (Nor) NOR (a nor a) nor b b nor b ((a ⊽ a) ⊽ (b ⊽ b)) ⊽ (a ⊽ b... ((a⊽a) ⊽ (b⊽b)) ⊽ ((a⊽a) ⊽ a... Wolfram Axiom (a nor a) nor (b nor b) ((a ⊽ a) ⊽ b) ⊽ ((a ⊽ b) ⊽ a... b ((a ⊽ a) ⊽ a) ⊽ ((a ⊽ a) ⊽ ... a ((a ⊽ a) ⊽ a) ⊽ ((a ⊽ b) ⊽ ... (a nor b) nor (a nor b) ((a ⊽ a) ⊽ a) ⊽ ((a ⊽ a) ⊽ a...

Boolean

This webmix covers the Boolean functions that are used to formulate logic with variables which are truth values and used in describing logical relational models of theories with a notion of structure.

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