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Logic Gates (AND, OR, NOT)

The fundamental physical and mathematical components of digital electronics. They implement basic Boolean operations: Y=A∧BY = A \land B, Y=A∨BY = A \lor B, Y=¬AY = \neg A.
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The statement of the theorem

Define the fundamental Boolean operations Y=f(A,B)Y = f(A, B) using the following formal definitions: \n1. AND Gate (Conjunction): Y=A∧B={1if A=1 and B=10otherwiseY = A \land B = \begin{cases} 1 & \text{if } A=1 \text{ and } B=1 \\ 0 & \text{otherwise} \end{cases}\n2. OR Gate (Disjunction): Y=A∨B={0if A=0 and B=01otherwiseY = A \lor B = \begin{cases} 0 & \text{if } A=0 \text{ and } B=0 \\ 1 & \text{otherwise} \end{cases}\n3. NOT Gate (Negation): Y=¬A=1−AY = \neg A = 1 - A (assuming B={0,1}\text{B} = \{0, 1\}). These operations are idempotent, commutative, and associative.