The term intersection for GLB should not be used here as if we take intersection {1,2,3} and {1,3,5} , then it will give us {1,3}.
In the same way the term union for LUB is not correct as {1,2,4}+{1,2,3} gives {1,2,3,4} which is not even there in this POSet.
The operaion set containment . It's like if y(- {x,y,z,w} , then y belong or contained in this set.
so no need to discuss about LUB as (1,2,3,4,5} and every element of this Hasse diagram is present/contained in this set.
In the same way for GLB I need to check only two pairs :
Pair 1: {1,2,3) and {1,2,4} = only 1 can satisfy the GLB
Pair 2: {1,2,4} and {1,3,5} = LB are 1 and 1,3 . Here GLB is 1,3
For Pair1, definitely I need to include 1 else GLB for pair1 won't be satisfied.
For Pair2, I can include {1,3} but does it necessary because here the operation is containment.
So , 1(- {1,3,5} which , in other words 1 belongs to set {1,3,5}. Then no need to add {1,3}
So , adding 1 as GLB would be suffice to make it Lattice.