These are not possible, as x can be 7 only if y is 7, and likewise for 8. Semantics isn't based on sets, but on non-deterministic assignments to variables: y is either 7 or 8 and x is either y or 2.

(7, 8) and (8, 7) are not possible because:

If x = 2 then clearly (x, y) is not (7, 8) or (8, 7) because 2 is not 7 or 8.

If x = y then (x, y) is (7, 7) or (8, 8).

It can't be either of those, because any given outcome is forcing a single value of y (or any variable in general).

Edit: Ah... I see now.

By that logic, how is either (7,7) or (8,8) allowed?

"x:=(y|2); y:=(7|8); (x|y)"

translates (roughly) to:

(x|y) is a cartesian product--the set of all ordered pairs (X,Y) such that X is in x and Y is in Y, in order.

x has 2 elements: X=y and X=2.

y has 2 elements: Y=7 and Y=8.

So the set of all ordered pairs is (X=Y, Y=7), (X=Y, Y=8), (X=2, Y=7), (X=2,Y=8).

Since X=Y in the first two pairs, replace it with the value of Y from that pair: (X=7,Y=7), (X=8,Y=8).

It's an exclusive or. So if x is y that is 7, then it can't be 8.

y can't be both 7 and 8 at the same time. It's either one or the other.

I was confused by this too.