Question

Q.7.In the lattice D30. The complement of 5 is
a) 2
b) 3
c) 6
d) 15​

Answer 1

Answer:

6......................

Answer 2

(c) 6

In a Complemented Lattice each element has at least one complemented.

1. 1∨30 =30                  1∧30 = 1          1' =30 and 30'=1
2. 2∨15 = 30                 2∧15 = 1           2'=15 and 15'=2
3. 3∨10 = 30                  3∧10 = 1          3'=10 and 10'=3
4. 5∨6 = 30                    5∧6 = 1             5'=6 and 6'=5

Here Every element has one element hence,it is a complemented Lattice. In a Distributive Lattice complement of an element if exists is unique i.e. each element has at most one element.

Here in D30 Every element has unique  complement.Hence, it is Distributive Lattice.