Check if one condition includes another

I have two conditions A and B in a form of “ast tree”. How can I check that B is more strict than A? I.e. if B is true then A is always true.

Example

A: x = 1 and (b = 2 or c = d)

B: y = 5 and x = 1 and (b = 2 or c = d)

Does B include A -> true


A: x = 1 and (b = 2 or c = d)

B: y = 5 and x = 1 and (b = 2 or c = d)

Does B include A -> false


This seems to be a common task for a specialist in logical math. But I have only very basic knowledge about logical arithmetics. Any articles/studies about subject appreciated.