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My doubt is in second hasse diagram for (I,g) lub should be I and j so it is not lattice please correct me if i amwrong 

in Set Theory & Algebra by Loyal (5.7k points)
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For I and G LUB is 'I' and it is a lattice per me

What is the answer given ?
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My doubt is in second hasse diagram for (I,g) lub should be I and j 

No, $LUB(i,g) = i$ because $i \leq j$ 

And It's an valid lattice But the Hasse diagram has one extra edge $(g-j)$ which could be removed because it is implied by the Transitivity. 

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@deepak bro if it was lattice given directly then they wouldn't give one extra edge (g−j) which is forming transitivity

Right ?

Here they are asking that which one is lattice that's why we are saying that yeah it is eligible for lattice if we remove that transivity because it is already implied

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