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Transcript 
Theorem 2
Uniqueness of Complement: For every a in B, its
complement a' is unique.
Proof: We prove by contradiction.
Suppose that a’ is not unique, i.e. a1', a2' in B & a1' ≠a2’.
We have a1' = a1' * 1 (Postulate 3)
= a1' * (a + a2') (Postulate 4)
= (a1' * a) + (a1' * a2') (Postulate 2)
=
0
+ (a1' * a2') (Postulate 4)
= a1'*a2' (Postulate 3).
Likewise, we can also prove the same with a2', i.e.
a2' = a1'*a2'.
Consequently, we have a1' = a2', which contradicts
our initial assumption that a1' ≠a2'.
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