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?

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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).