Source: p 158. Sweet Reason: A Field Guide to Modern Logic (2010 2 ed) by Henle, Garfield, Tymoczko.
[...] Call this Information Implication. Its truth table looks like this:
This question focuses on the 5 rows numbered in red above. I already understand how to conclude the Truth Values for ⟹; so please do not answer with formal proofs or Truth Tables.
My problem: they still feel counterintuitive. So can they be intuited or explained directly, without relying on the intermediate step (B → S) ≡ (¬B ∨ S)? For example, consider 8 and 12: how does it make intuitive sense for the Truth Value to differ from A's or B's?