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GATE CS 2017 Set 2 — Question 21

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NAT+1 / -0MediumPartial Orders & LatticesSets & CombinatoricsEngineering Mathematics

Engineering Mathematics → Sets & Combinatorics → Partial Orders & Lattices

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Question

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