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Complement of an element $x$  is said to be $y$, iff Lowest Upper bound of $x$ and $y$ is the upper bound of lattice and Greatest Lower bound is the lower bound of lattice.

In the above lattice, Upper bound $ = h$ and Lower bound $= a$. So, two elements are complement of each other only if their LUB and GLB are $h$ and $a$ respectively.

$LUB(c,f) = h$ and $GLB(c,f) = a$. So, $a$ and $f$ are complement of each other.

$LUB(e,f) = f \ne h$ and $GLB(e,f) = e \ne a$.

$LUB(d,g) = h$ and $GLB(d,g) = c \ne a$.

Hence, Option (B) and Option (C) are not correct.

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 A complemented lattice is a bounded latice (with least element  0 (a here) and greatest element 1(h here), in which every element a has a complement, i.e. an element b satisfying a ∨ b = 1 and a ∧ b = 0.  then b is called complement of a.

Complement of e is not f since (e v f) $\neq$ h.

Complemet of any element can not present on same side . like here e and f are on same side which create problem i.e.

 (e v f) $\neq$ h.

Complement of d is not g since (d $\wedge$ g) $\neq$ a. so it is false

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