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Let [N,\leq] is a partial order relation defined on natural numbers. Identify the false statement?

(A). [N,\leq] is distributive but not complemented lattice

(B). [N,\leq] is not a lattice

(C). [N,\leq] is not Boolean lattice

(D). Element 1 doesn't have complement

in Mathematical Logic by (290 points) | 30 views
Is the answer B?

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

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

1 Answer

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  1. Not a lattice
by (1.6k points)
edited by
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)
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.
Vimal has the right interpretetion of my sentence..

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