**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?**b) not comparable

a) 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**b) Addition, subtraction

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**