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Boolean Algebra: Can't prove that ô.e+ô.ê+o.e=ô+e (the accent means negation).

  1. Feb 8, 2012 #1
    Consider a Boolean algebra (B,+,.,negation symbol). 0 is the zero element and 1 is the unit element. + has the lowest precedence and negation has the highest. Show that ô.e+ô.ê+o.e=ô+e for all o and e in B.

    This isn't a logic gate algebra because that'd be easy, so I can't use the values 0s and 1s to prove this. I can only use the Boolean algebra laws:
    Double Complement law
    Idempotent law
    Identity law
    Domination law
    Commutative law
    Associative law
    Distributive law
    De Morgan's law
    Absorption law
    Unit property
    Zero property

    This is one of my attempts and I got pretty close but still pretty close isn't the answer.
    PHP:

     ô.e+ô.ê+o.e
    =ô.(e+ê)+o.e      cause of distributive law
    =ô.1+o.e       cause of unit property
    =ô.o+ô+o.e      1=o+ô cause of unit property, I'm unsure as to whether o+ô should be in brackets but I assumed not
    =0+ô+o.e      cause of zero property
    =o.ô+ô+o.e      0=o.ôcause of zero property
    =o.ô+o.e+ô        cause of commutative property
    =o.(ô+e)+ô        cause of distributive property
    I didn't know what to do at this point.
     
  2. jcsd
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