Discussion
Which one of the following options is not a property of Boolean Algebra?
Note: + is OR operation, . is AND operation, and ′ is NOT operation
Answer: B
The statement that is not a property is \(a\,.\,a' = 1\).
A variable ANDed with its own complement is always 0, never 1: if a = 1 then a′ = 0, and if a = 0 then the AND is 0 anyway. This is the complement law a . a′ = 0.
The other three are genuine laws of Boolean algebra: a + b = b + a and a . b = b . a are the commutative laws for OR and AND, and a + a′ = 1 is the complement law for OR, since one of a and a′ is always 1.
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