In Theorem 12.3, we showed that [ and \ satisfy the distributive properties: A [ .B \ C

Chapter 59, Problem 59.7

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In Theorem 12.3, we showed that [ and \ satisfy the distributive properties: A [ .B \ C / D .A [ B/ \ .A [ C / and A \ .B [ C / D .A \ B/ [ .A \ C /:These equations can be rewritten with ^ in place of \ and _ in place of [:a _ .b ^ c/ D .a _ b/ ^ .a _ c/ anda ^ .b _ c/ D .a ^ b/ _ .a ^ c/: Give an example of a lattice for which the distributive laws are false

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