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

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Lakshman Patel RJIT
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in Set Theory & Algebra
Oct 6, 2018

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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}.

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