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GO Classes Weekly Quiz 10 | Discrete Mathematics | Set Theory, Mathematical Logic, Lattice | Question: 5

in Set Theory & Algebra edited by
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Let $(L, \#)$ be a lattice, where $\#$ is some relation defined on the base set $x,y,z \in L.$ Then for all Which of the following is/are necessarily true?

  1. $x \vee y = y \vee x$
  2. $x \vee (x \wedge y) = x$
  3. $x \vee (y \wedge z) = (x \vee y) \wedge (x \vee z)$
  4. $x \wedge (x \vee y) = x$
in Set Theory & Algebra edited by
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A is commutative and B,D is absorption.
C is Distributive. only special lattice follow this property.

Edit: wrote associative instead of absorption. Thnx @Amlan Kumar Majumdar for pointing out. 

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I think B and D is absorption Law.
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1 Answer

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Every lattice satisfies commutative, associative, idempotent, consistency, absorption laws

C: This is distributive, not all lattices are distributive.
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