A sublattice(say, S) of a lattice(say, L) is a convex sublattice of L if

Question

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x<=y<=z, where x, y in s implies z in s, for every element x, y, z in l

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x>=z, where x in s implies z in s, for every element x, y in l

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x=y and y<=z, where x, y in s implies z in s, for every element x, y, z in l

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x=y and y>=z, where x, y in s implies z in s, for every element x, y, z in l

Q. A sublattice(say, S) of a lattice(say, L) is a convex sublattice of L if