# 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. $(\top \setminus X)\sqcap^{\mathsf{FCD}} Y = (\top \setminus X)\sqcap Y$.

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