[Math] Whether Subset of a Power Set is a Lattice

Question

$A=$ countably infinite set
$p(A)=$ power set of $A$
$p(A)$ is uncountably infinite

I have this question as book i am using explicitly mentioned it as A:finite set

now, poset $(P(A)$,subset) is it a lattice?

I know what a lattice is and according to definition any partial order relation on uncountably infinite set where each element has a LUB,GLB should be counted as a lattice.

Answer 1

For every set $X$ the power set $\mathcal{P}(X)$ together with the subset relation $\subseteq$ forms a complete lattice. I explained this recently here as part of another answer.