good question :)
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to prove that a lattice is dual we have to prove that it is a POSET
for reference -> https://en.wikipedia.org/wiki/Duality_(order_theory)
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for power set:
1)reflexive : every set is a subset of itself. so its reflexive
2)anti symmetric: if a is subset of b and b is a subset of a means a and b are equal(reflexive). so it is antisymmetric as a is subset of b doesnt means b is a subset of a .
3)transitive: a is subset of b and b is subset of c means a is subset of c.
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which is a POSET. hence dual is option C (as the posets <P,R> and <P,R-1> are called DUALS.