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let L be the four- element lattice <{0,a,b,1},⋁,⋀> where 0 is the least element,1 is the largest element, and a⋀b=0, a⋁b=1 (the hasse diagram is figure 1(c)). show that L has the universal mapping property for the class of lattices over the set {a,b}.

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Do you know the definition of "the universal mapping property for the class of lattices over the set {a,b}"? If not, then this should be part of your question. If you do know what the universal mapping property is, then this is easy to prove directly from the definition. What have you tried? Where did you get stuck? – William DeMeo Dec 29 '12 at 22:32
Also, your question refers to figure 1(c), but there is no such figure. This and the formatting of the math ssymbols in your question seem to indicate that you have copied the question from somewhere. In that case, please provide a reference, and if this question is homework, tag it as such. – William DeMeo Dec 29 '12 at 22:44

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