GATE 2005 on Lattice

The following is the Hasse diagram of the poset [{a,b,c,d,e},≺]

The poset is :

(A) not a lattice

(B) a lattice but not a distributive lattice

(C) a distributive lattice but not a Boolean algebra

(D) a Boolean algebra

Answer

Things You need to know

Refer: http://www.techtud.com/short-notes/lattice

Lattice  ∵ LUB and GLB exist for every-pair of element 

             ∴ The given POSET is a Lattice.

Distributive ∵ Each element of a distributive lattice has unique complement

                    ∴ The given POSET violates this property . Hence, is not Distributive lattice.

Ans. (B)

 

1Comment
abhinandan @abhinandan
24 Aug 2017 09:36 pm

 boolean algebra: a lattice l is called boolean algebra if it is distributive and complemented lattice. in other words in boolean algebra every element has a unique complemet.

in the above question the complement of element b are c & d. voilating the boolean algebra condition. hence option b is correct