# Radio airplay restrictions are nationally imposed regulations. The City Club has compiled a guide to all nationally i...

Julie on August 5, 2019

Argument Clarification

Hi LSAT Max, In the previous thread, there seems to be no clarity as to whether the argument in the stimulus is valid or invalid. Isn't the argument invalid because the existence of the necessary condition doesn't invoke the existence of the sufficient? It looks like the stimulus and the correct answer choice have that exact flaw by concluding the S cond. of the contrapositive (the guide covers restrictions/award the prize) because of the existence of the N cond. (no taxation and no labor laws/ not a shrub and native to N.A)(? I would appreciate for a third instructor to clear the confusion created by the instructors from the previous thread, thanks

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Irina on August 5, 2019

@Julie,

Thank you for bringing this up. I agree with @Ravi 's determination that it is a valid argument. I am going to use formal rules of inference to construct a proof for the conclusion.

The argument tells us that (all) radioplay restrictions are nationally imposed regulations:

(1) RAR -> NIR

P ->Q

The City club complied all nationally imposed regulations except taxation and labor law, so if it is a nationally imposed regulation it must be in the city guide unless it is related to taxation or a labor law:

(2) NIR & ~ (T v LL) -> CG

Q & ~(R v S) -> T

Radio airplay restrictions are related to neither taxation or labor law, so if it is a radio airplay restriction it is not in taxation or labor law category:

(3) RAR -> ~ (T v LL)

P-> ~( R v S)

Therefore, city guide covers airplay restrictions:

(4) RAR -> CG

P -> T

Let's put all the premises together:
(1) P ->Q
(2) Q & ~(R v S) -> T
(3) P-> ~( R v S)

C: P -> T

Per composition, (1) & (3) we can infer:

(5) P - > Q & ~ (R v S)

Using hypothetical syllogism, (5) & (2) we can infer:

(6) P-> T

This is the conclusion we set out to prove, and thus, this is a valid argument.

Does this make sense?

Let me know if you have any further questions.