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AND
A · B
True only if BOTH are true
A
B
Out
0
0
0
0
1
0
1
0
0
1
1
1
OR
A + B
True if AT LEAST one is true
A
B
Out
0
0
0
0
1
1
1
0
1
1
1
1
XOR
A ⊕ B
True if inputs are DIFFERENT
A
B
Out
0
0
0
0
1
1
1
0
1
1
1
0
Boolean Algebra Laws
De Morgan's Laws
(A · B)' = A' + B'
(A + B)' = A' · B'
Identity & Null
A · 1 = A | A + 0 = A
A · 0 = 0 | A + 1 = 1
Inverse & Idempotent
A · A' = 0 | A + A' = 1
A · A = A | A + A = A
Distributive
A(B+C) = AB + AC
A + BC = (A+B)(A+C)