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Left Distributive Law

Let \(A\) be a set , and let \(\ast:A \times A \rightarrow A\) and \(\star:A \times A \rightarrow A\) be binary operations . We say that \(\star\) left distributes over \(\ast\) provided for any \(a,b,c \in A\):

\[ a \star (b \ast c)=(a \star b) \ast (a \star c) \]