Truth Table For Logical Operations

AND operation:

p q p ∧ q
T T T
T F F
F T F
F F F

OR operation:

p q p ∨ q
T T T
T F T
F T T
F F F

Negation Operation:

p ∼ p
T F
T F
F T
F T

Conditional Operation

p q p ⇒ q
T T T
T F F
F T T
F F T

Biconditional Operation:

p q p ⇔ q
T T T
T F F
F T F
F F T

Tautology and Fallacy

p q ⇒q ⇒p (p⇒q)∨(q⇒p) ∼{(p⇒q) ∨(q⇒p)}
T T T T T F
T F F T T F
F T T F T F
F F T T T F

NAND Operation

p q p NAND q
F F T
F T T
T F T
F F T

NOR Operation

p q p NOR q
F F T
F T F
T F F
T T F

XOR Operation

p q p XOR q
F F F
F T T
T F T
T T F