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May 9, 2017 / porton

Three (seemingly not so difficult) new conjectures

I’ve noticed the following three conjectures (I expect not very difficult) for finite binary relations X and Y between some sets and am going to solve them:

  1. X\sqcap^{\mathsf{FCD}} Y = X\sqcap Y;
  2. (\top \setminus X)\sqcap^{\mathsf{FCD}} (\top \setminus Y) = (\top \setminus X)\sqcap (\top \setminus Y);
  3. (\top \setminus X)\sqcap^{\mathsf{FCD}} Y = (\top \setminus X)\sqcap Y.
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2 Comments

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  1. porton / May 9 2017 22:07

    I’ve proved the first one. I am going to publish the (easy) proof soon.

  2. porton / May 9 2017 22:47

    All three conjectures follow from the fact that \Gamma is a sublattice of \mathsf{FCD}.

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