Let L be a set with relation R which is transitive, anti-symmetric and reflexive and for any two elements a,b ∈ L let the least upper bound lub(a,b) and greatest lower bound glb(a,b) exist. Which of the following is/are true?
a. L is a poset.
b. L is a boolean algebra.
c. L is a lattice.
d. None of the above.
(A) a, b
(B) a, c
(C) only c
(D) only b
Answer: (B)
Explanation: A is true since By definition, a Relation is said to be a POSET if it is reflexive, transitive and anti-symmetric.
C is true since by definition, a POSET is a lattice if every pair of elements has a greatest lower bound and a least upper bound.
Quiz of this Question