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Logic question

Posted on 2012-03-15
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Last Modified: 2012-03-19
Hi, i have a logic worksheet. I am have trouble with this question:

A binary operator (+) distributes from the left overt another binary operator (x) precisely when the equation x (+) (y (x) z) = (x (+) y) (x) (x (+) z) always holds. Using a truth table, check the following (the answer should include the truth table as well as its interpretation w.r.t. the question):

(a) Does => distribute from the left over /\ ?
(b) Does /\ distribute from the left over => ?

could someone please work me through the solution please?
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Question by:jillette
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by:ozo
ID: 37727889
A binary operator (=>) distributes from the left overt another binary operator (/\) precisely when the equation x (=>) (y (/\) z) = (x (=>) y) (/\) (x (=>) z) always holds.

Does it always hold?
Can you demonstrate that with a truth table for all possible values of x, y, and z.
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by:jillette
ID: 37737756
i dont understand the phrase  "left over another binary operator". can you please explain this to me. also by  "always hold" do you mean thatx (=>) (y (/\) z) will equal the same as (x (=>) y) (/\) (x (=>) z).

Thank you
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ozo earned 500 total points
ID: 37739783
The above statement defines what "distributes from the left" means.
The question does not require you to understand the the distinction between left and right,
but to illustrate, if it had been right instead of left, it might have said

A binary operator (+) distributes from the right over another binary operator (x) precisely when the equation  (y (x) z) (+) x = (y (+) x) (x) (z (+) x) always holds.

Always holds means that the equation is always true.
= means will equal the same as, so
A binary operator (=>) distributes from the left over (/\) if
x (=>) (y (/\) z) will always equal the same as (x (=>) y) (/\) (x (=>) z).
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