# Graphs – Lattices

1. A Poset in which every pair of elements has both a least upper bound and a greatest lower bound is termed as _______
a) sublattice
b) lattice
c) trail
d) walk

2. In the poset (Z+, |) (where Z+ is the set of all positive integers and | is the divides relation) are the integers 9 and 351 comparable?
a) comparable
b) not comparable
c) comparable but not determined
d) determined but not comparable

.

3. If every two elements of a poset are comparable then the poset is called ________
a) sub ordered poset
b) totally ordered poset
c) sub lattice
d) semigroup

.

4. ______ and _______ are the two binary operations defined for lattices.
a) Join, meet
c) Union, intersection
d) Multiplication, modulo division

5. A ________ has a greatest element and a least element which satisfy 0<=a<=1 for every a in the lattice(say, L).
a) semilattice
b) join semilattice
c) meet semilattice
d) bounded lattice

.

7. A sublattice(say, S) of a lattice(say, L) is a convex sublattice of L if _________
a) x>=z, where x in S implies z in S, for every element x, y in L
b) x=y and y<=z, where x, y in S implies z in S, for every element x, y, z in L
c) x<=y<=z, where x, y in S implies z in S, for every element x, y, z in L
d) x=y and y>=z, where x, y in S implies z in S, for every element x, y, z in L

.

9. Every poset that is a complete semilattice must always be a _______
a) sublattice
b) complete lattice
c) free lattice
d) partial lattice

.10. A free semilattice has the _______ property.
a) intersection
b) commutative and associative
c) identity
d) universal