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1) in a complemented lattice , every element will have at least one complement and in distributive lattice , every element will have maximum one complement , now you can think if lattice is complemented and distributive both then , in this every element will have exactly complement.

2) first it was considered that if in a lattice , every element has one unique complement then it will be distributive lattice , which was later disproved by this man dilworth

https://www.researchgate.net/publication/317565891_Lattices_with_unique_complementation

so second statement is false.