**1. Hasse diagrams are first made by ______**a) A.R. Hasse

**b) Helmut Hasse**

c) Dennis Hasse

d) T.P. Hasse

**2. If a partial order is drawn as a Hasse diagram in which no two edges cross, its covering graph is called ______a) upward planar**b) downward planar

c) lattice

d) biconnected components

**3. If the partial order of a set has at most one minimal element, then to test whether it has a non-crossing Hasse diagram its time complexity __________a) NP-complete**b) O(n

^{2})

c) O(n+2)

d) O(n

^{3})

.

**4. Which of the following relation is a partial order as well as an equivalence relation?a) equal to(=)**b) less than(<)

c) greater than(>)

d) not equal to(!=)

**5. The relation ≤ is a partial order if it is ___________a) reflexive, antisymmetric and transitive**b) reflexive, symmetric

c) asymmetric, transitive

d) irreflexive and transitive

**6. In which of the following relations every pair of elements is comparable?a) ≤**b) !=

c) >=

d) ==

**7. In a poset (S, ****⪯****), if there is no element n****∈****S with m<n, then which of the following is true?**a) an element n exists for which m=n

**b) An element m is maximal in the poset**

c) A set with the same subset of the poset

d) An element m is minimal in the poset

.

**8. In a poset P({v, x, y, z}, ****⊆****) which of the following is the greatest element?a) {v, x, y, z}**

b) 1

c) ∅

d) {vx, xy, yz}

.

**9. Suppose P _{1} is a partially ordered class and a cut of P_{1} is pair (D, T) of nonempty subclasses of P_{1} satisfies which of the following properties?**b) D∪T=P

a) D∩T=Ø

_{1}

c) xyz∈T

d) z∈T and zx∈D

.**10. Let G be the graph defined as the Hasse diagram for the ⊆ relation on the set S{1, 2,…, 18}. How many edges are there in G?**a) 43722

**b) 2359296**

c) 6487535

d) 131963