It seems to me that the 'implies' in English language does not mean the same thing as the logical operator 'implies', in a similar way how 'OR' word in most cases means 'Exclusive OR' in our everyday language use.Let's take two examples:If today is Monday then tomorrow is Tuesday.This is true.But if we say:If the sun is green then the grass is green.This is also considered true. Why? What is the 'logic' in natural English behind this? It blows my mind.
Why is A implies B true if A is false and B is false?
terminology;logic;first order logic;propositional logic