The complement(s) of the element 'a' in the lattice shown in below figure is…

In a lattice, an element x is called a complement of a if:

a∨x=1

and

a∧x=0

From the diagram:

• Top element = 1

• Bottom element = 0

Checking elements b,c,d,e:

• a∨b=1 and a∧b=0

• a∨c=1 and a∧c=0

• a∨d=1 and a∧d=0

• a∨e=1 and a∧e=0

Thus, all four elements b,c,d,e are complements of a.

Therefore, number of complements of a is:

4