How to calculate the logical expression of this logical variable?

Because there are few variables (only x and y), it can be solved by truth table or Karnaugh map. This is the first method; Second, it is a more general expression-transformation by logical algorithm.

X+X′Y； (X stands for: the negation of X)

= X * 1+X′Y； (anti-identity; * stands for: and operator)

= X *(Y+Y′)+X′Y； (law of excluded middle inversion)

=(XY+XY’)+X’Y； (distribution law)-If you are familiar with it, the first three steps can be achieved in one step; At this time, we should see that it is equal to (x+y)-they are all equal to:1-x' y';

=(XY+XY′)+(XY+X′Y)； (Inverse idempotent law, commutative law, associative law)

= X+Y； (Anti-distribution Law, law of excluded middle, Invariance Law)

The third method: If you are familiar with the relationship between the value of a logical expression and the true value of a logical proposition (or the on-off of a logical circuit), you can do this:

X+X'Y: indicates that X is true, and there is no requirement for Y at this time (that is, Y is true or false); Or x is false, in which case y must be true; In short: at least one of X and Y is true (that is, both are allowed to be true).

Obviously, this is the definition of OR operation; That is equivalent to x+y.