Which one of the following is an acceptable schedule for the evening's performers, from first through seventh?

jiselyonaira August 3, 2019

Only If?

Rule #3 states "L performs 3rd only if N performs 5th. would that mean: if N performs 5th then L performs 3rd. N5 --> L3? why is the set up in the video L3 --> N5

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Irina August 4, 2019

@jiselyonaira,

The video diagram is correct. "Only if" generally introduces a necessary condition, so in a statement:

A only if B,

B is a necessary condition, thus if B is false, A is also false:

~ B - > ~A
~N5th -> ~L3d

and A is a sufficient condition, thus if A is true, B must also be true:

A -> B
L3d -> N5th

Does this make sense?

Let me know if you have any further questions.

AneeshU August 7, 2020

PLEASE DON'T READ THIS UNLESS YOU'RE ALREADY CONFUSED

Hi, I understand your explanation and also why L3 --> N5 however, I would like to know if my understanding is correct in relation to use of the word 'only' (case 2) and why the reverse is not true (case 1).

Case 1: Lalitha is 3rd only if Norton is 5th = L3-->N5 (Me: I am not able to see why N5-->L3 cannot be proved. Although this would usually be a mistaken reversal, according to my understanding, the rule states that Lalitha is 3rd in 'only' one scenario - when Norton is 5th, therefore Norton being 5th is also sufficient for Lalitha to be 3rd and mistaken reversal would not apply. Rephrasing, if Norton is 5th, there is no scenario where Lalitha is not 3rd. If the rule was framed 'Lalitha can be 3rd only if Norton is 5th', then I see how that would be a mistaken reversal.

Case 2: If the rule was 'Lalitha is 3rd if Norton is 5th' = N5--> L3 and could also be rephrased as 'If Norton is 5th, Lalitha is 3rd'

So, 'only' reverses the relation between the two conditions? Could you please explain this with an example? I've finished studying sufficient and necessary conditions and have trouble remembering the indicators for the two conditions without understanding the logic behind them. What am I missing here? The problem is not that I don't understand the right answer, but that I'm unable to disprove the incorrect one.