DM-Groups and Lattice-Q12

+1 vote

Let (L,\leq) be a lattice. Then for all x,y,z\in L which of the following is FALSE?

(A).x\lor y = y\lor x

(B).x\lor (x\land y) = x

(C).x\lor (y\land z) = (x\lor y)\land(x\lor z)

(D).x\land (x\lor y) = x

asked Jul 8 in Discrete Maths by gbeditor (4,440 points)
reshown Jul 9 by gbeditor

2 Answers

0 votes
 
Best answer

Here \leq represents any relation, Not less than or eqal to specifically. Lattice might not satisfy distributive property so Option C is false. 

answered Jul 11 by getgatebook (25,720 points)
0 votes
{L,<=} is tos and all tos is always distribute lattic.

And all lattice follow Identity property , associative,commutative, absorption

But not distributed property if a lattice follow distributed property than this type of lattice called distributed lattice.

Here given lattice is tos and tos always follow all these propertie so I think all option are wrong.

Please correct me if my statement is wrong.
answered Jul 9 by tsnikhilsharmagate2018 (17,270 points)
why a lattice will follow C?
you are absolutely correct. i too have same dilemma. i think all options are correct
@tsutkarsh
Not all lattice follow c but given lattice follow all propertie
I think it is not a description but just a notation. Every lattice may or may not follow the distributed property. I think option C is right.
Yes exactly

That less than equal to sign denotes comparability between two elements in a poset
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