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Let  is a partial order relation defined on natural numbers. Identify the false statement?

(A).  is distributive but not complemented lattice

(B).  is not a lattice

(C).  is not Boolean lattice

(D). Element 1 doesn't have complement

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BECAUSE IT IS A LATTICE.(it formas a chain)

But can u tell me what is the definition of boolean lattice?
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They mean “Boolean algebra”: A lattice that is both complemented and distributive.

1. Not a lattice
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Can you explain why is it not a lattice? For any two elements we have LUB and GLB right? (The selected elements themselves would be meet and join)
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I think He is saying that statement of option $(B)$ is false and hence is the answer too.

$(A)$ given lattice is distributive but it is not a complemented lattice. Because complemented lattice must be bounded and each element must have at least one complement.So, → $True$

$(B)$ this is not a lattice. $\rightarrow False$

$(C)$ This is not a boolean lattice. $\rightarrow True$

because, In boolean lattice every element has complement. This is not true in given lattice.

$(D)$ $1$ has not a complement. It’s true infact in our lattice no element is having a complement. So $\rightarrow True$

So false statement is $(B)$ and hence answer.
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@sambhrant
Vimal has the right interpretetion of my sentence..

Gaitonde ko english nehi ata utna a66a..samajh lena bhai..