@jhlaier Good catch! In this case I was just using “if” to demonstrate the logical form (A → B), not to analyze the actual wording. (“if A, then B” represents how a sufficient condition triggers a necessary one.) I totally get that “only if” introduces the necessary condition though.

It took me a while to understand the Kumar example, but what finally made it click was focusing on the LAWGIC language instead of the words themselves.

If A then B is valid

If B then A is invalid

VALID

(A) If Cited Late then

(B) Must have arrived 5 min past the bell

INVALID

(B) If arrived 5 min past the bell then

(A) you must be cited late

Why puppies? I love puppies.