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The complement(s) of the element 'a' in the lattice shown in below figure is (are) ____

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c,b,e,d

• $lub(a,e) = lub(a,b) = lub(a,c) = lub(a,d) = I$ (Upper Bound of Lattice)
• $glb(a,e) = glb(a,b) = glb(a,c) = glb(a,d) = O$ (Lower Bound of Lattice)

So, $e, b, c, d$ all are complement of $a.$

by Boss (16.3k points)
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How b is possible to complement of a..I don't get it
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@mr robot

lub(a,b)=I (Upper Bound of Lattice)

glb(a,b)=O (lower Bound of Lattice)

LUB of $a$ and $\overline{a}$ must be $I$

GLB of $a$ and $\overline{a}$ must be $O$

where $I$ is the upper bound, and where $O$ is the lower bound

All of d,b,c,e qualify to be $\overline{a}$

by Loyal (6.6k points)
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Can $I$ and $O$ also be complements? What are the LUBs and GLBs of $\{a, I\}$ and $\{a, O\}$?

Edit: Okay cleared self-doubt: GLB of first one is $a$ itself, not the LB of the lattice, so they are not a complement pair. Similarly for the LUB of the second.