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A) {0,g,h,i}

B) {0,h,s}

C) {d,e,f,g,h,i,0}

D) {0,h,e}

e is not the lower bound in both $L$ and $R$ so eliminate option c and d

g is lower bound of both so you can mark $A$ but still you can check others and $A$ is correct

How to find Lower bound and Upper bound?

in simple words, x is a lower bound to y means, in hasse diagram, you should reach from x to y.

lower bounds of a = {d,e,g,h,i,o} but note that f is not lower bound of a due to you can't reach a from f.

lower bounds of b = {d,f,g,h,i,o} but note that e is not lower bound of b due to you can't reach b from e.

lower bounds of {a,b} = lower bounds of a ∩ lower bounds of b = {d,g,h,i,o} = L

lower bounds of b = {d,f,g,h,i,o} but note that e is not lower bound of b due to you can't reach b from e.

lower bounds of c = {e,f,g,h,i,o} but note that d is not lower bound of c due to you can't reach c from d.

lower bounds of {b,c} = lower bounds of b ∩ lower bounds of c = {f,g,h,i,o} = R

L ∩ R = {d,g,h,i,o} ∩ {f,g,h,i,o} = {g,h,i,o}.

L: lower bound of {a,b} is {d,g,h,i,o}

R: lower bound of {b,c} is {f,g,h,i,o}

so L∩B is {g,h,i,o}

which satisfies option a

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can anyone, give the answer, how to find Lower bound and Upper Bound in given Hasse diagram?

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