A ring of gas emitting X-rays flickering 450 times per second has been observed in a stable orbit around a black hole...

Dalaal April 25, 2020

Prior explanation

Could you explain the conditional reasoning behind diagramming the statement "that rate of flickering can best be explained if the ring of gas has a radius of 49 kilometers"? Isn't the 49 km radius the sufficient condition? why was it diagrammed as necessary in your explanation?

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shunhe April 27, 2020

Hi @Dalaal,

Thanks for the question! So the statement that you point to isn’t really needed in getting the correct answer choice here. But one way to diagram that second sentence is certainly the following:

ring of gas has radius of 49 km —> rate of flickering best explained

which would put that clause in the sufficient condition, as you discussed.

But as stated, that part isn’t important to getting to the answer choice here. The only two things that we need are the first sentence and the third sentence. The first sentence tells us:

Maintains an orbit

And the third sentence tells us (remember, we diagram X unless Y as ~Y —> X):

~black hole spinning —> gas ring could not maintain an orbit so close to a black hole

and the contrapositive of that is

Maintains an orbit —> Black hole spinning

And so since we know that the ring of gas maintains an orbit, then the black hole is spinning, which is what (C) tells us.

Hope this helps! Feel free to ask any other questions that you might have.

aseikhon11 July 1, 2020

wouldnt the contra positive be black hole not spinning?