Consider the set $X = \{a,b,c,d,e\}$ under the partial ordering $$R = \{(a,a),(a,b),(a,c),(a,d),(a,e),(b,b),(b,c),(b,e),(c,c),(c,e),(d,d),(d,e),(e,e)\}.$$ The Hasse diagram of the partial order $(X,R)$ is shown below. The minimum number of ordered pairs that need to be added to $R$ to make $(X,R)$ a lattice is _________ .

Consider the set X = \a,b,c,d,e\ under the partial ordering R = \(a,a),(a,b),(a,c),(a,d),(a,e),(b,b),(b,c),(b,e),(c,c),(c,e),(d,d),(d,e),(e,e)\. The Hasse diagram of the partial order (X,R) is shown below. The minimum number of ordered pairs that need to be added to R to make (X,R) a lattice is …

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