How would one, as intuitively as possible, explain

*why* the following implication is false

I understand that for

either the statement

or

must be true. Suppose the statement

is true; the falsity of the implication is quite apparent then. If the statement

is true then the veracity is apparent. Thus the implication is only true for one statement of the two within

.

However, the following implication is surprisingly true:

How come? Suppose

on the right-hand side of the implication is true; that implication is false! The implication is only true if

on the right-hand side. Once again, the implication is only true for

*one* statement of the two within

. In spite of this, we still claim that the implication as a whole is true whereas the first one is not.