DeMorgans law

Discussion in 'Homework Help' started by mannik, Nov 26, 2004.

  1. mannik

    Thread Starter New Member

    Nov 26, 2004
    3
    0
    Hi

    My teacher is a m*ron he won't (or can't) explain following:

    I have to find the complement of AB. The B have a bar over (inverted but I dunno how to do it in the forum) Can somebody explain to me how this is going on?

    Tommy
     
  2. Perion

    Active Member

    Oct 12, 2004
    43
    1
    Just use an apostrophe ' character after the term instead of the bar to show the complement - like, AB' which reads "A and not B"

    So - DeMorgan says:

    not (x and y) = (not x) or (not y)
    not (x or y) = (not x) and (not y)

    Or, using the ' symbol for NOT and the usual AND and OR symbol conventions, DeMorgan is written:
    (xy)' = x' + y'
    (x+y)' = x'y'

    In other words just take the complement of each individual term and change the AND to an OR (or vice versa).

    So, for the complement of AB':

    (AB')' = A'+ B (complement each term and change the AND to an OR)

    Let:
    A = "I am stupid"
    B = "I am tall"

    Then:
    AB' = "I am stupid and I am not tall"

    The complement of the above statement could be read something like:
    (AB')' = A' + B = "Either I am not tall or I am stupid"

    BTW - for me, AB :lol:

    Perion
     
  3. mannik

    Thread Starter New Member

    Nov 26, 2004
    3
    0
    Thank you very much for your help, now it make sence here you can see my teacker's answer:

    NOT(A and (NOT B)) = NOT A or NOT(NOT B) = NOT A or B

    ‘(AB’) = a’ + ‘(B’) = A’ + B

    But he was unable to explain it :angry:

    Again thx.

    Tommy

    BTW you might be tall - but I don't believe that you are stupid !!

    tommy
     
  4. Perion

    Active Member

    Oct 12, 2004
    43
    1
    You're welcome.

    See logic is (easy)' :)

    Best wishes,
    Perion
     
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