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Lattice

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First of all , we should know what a bounded lattice is :

A bounded lattice is a lattice in which we have two extreme elements known as least and greatest such that all other elements lie in in between .. i.e. for any other point 'x' in a lattice :

a) LUB of x and the topmost element(represented by 1) will give the greatest element..

b) GLB of x and bottommost element(represented by 0) will give the least element.

Now two elements x and y are complementary iff  : 

a) GLB of x and y leads to 0(least element)

b) LUB of x and y leads to 1(greatest element)

Now if we consider least and greatest element itself ..

a) LUB of least element and greatest element :  Greatest element

b) GLB of least element and greatest element : Least element

And for a bounded lattice , both greatest and least element will be present for sure..

Thus greatest element and least element are complementary to each other and hence the statement is true.

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