jillette

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# Logic question

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?

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?

ASKER

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

Thank you

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Does it always hold?

Can you demonstrate that with a truth table for all possible values of x, y, and z.