State number of partial order relations $U$ on $\{a,b,c,d\}$ such that $bUa,cUa,dUa$ and some other conditions.

Question

$\require{cancel}$

State how many possible partial order relations $U$ are there on the set $\{a,b,c,d\}$ such that

• $bUa, cUa, dUa;$ and
• $b\cancel U c, c\cancel U b, d\cancel U b \text{ and } b\cancel U c$.

How should I tackle this question?

A relation is Partial Order relation if it is Reflexive, Anti-Symmetric and Transitive