Hi FreshScale,You're reacting to Shashwat_hai's line that "
A only if B" becomes
A → B, and that's exactly the piece worth slowing down on. The trick is that the words "if" and "only if" point in
opposite directions.
The rule:- "A
if B" → B is enough to guarantee A →
B → A- "A
only if B" → B is
required for A; without B you cannot have A →
A → BThe phrase after "only if" is always the
necessary condition. Whatever comes after "only if" is the thing you can't do without.
Feel it with an everyday sentence:"You can graduate
only if you pass the final."
Does graduating force you to have passed? Yes - no pass, no graduation. So
graduate → passed. Notice it does
not run the other way: passing the final doesn't guarantee you graduate (you might fail another requirement). That's precisely
A → B, not
B → A.
Now map it back to E. Let A = "conditions are beneficial" and B = "water is not acidic." E says:
"conditions are beneficial to turtles
only if the water is not acidic"
Thereforebeneficial → not acidic (A → B). Take its contrapositive:
acidic → not beneficial. Wallakim's water
is acidic, so its conditions are
not beneficial - and since a thriving population needs beneficial conditions, Wallakim can't have one. That's the bridge the argument was missing.
Quick self-test - turn the one knob:- "Beneficial conditions
if the water is not acidic" → which direction? (not acidic → beneficial - that's actually choice A, the wrong one!)
- "Beneficial conditions
only if the water is not acidic" → beneficial → not acidic (choice E).
See how flipping "if" ↔ "only if" flips the arrow - and how that's exactly the difference between the trap answer A and the correct answer E.
Answer: EFreshScale
can you explain how is E: A only if B deduces to A -> B??