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Question states:

T won’t be selected only if G is selected. it must be true that...

- G → T
OR
G → - T

Arcade says it must be true that - G → T
----
Only if G is selected would T not be selected. Therefore, if G then no T (G → - T)

How can it be true that if no G is selected that T has to be selected?

[noah]

Question states:

T won’t be selected only if G is selected. it must be true that...

- G → T
OR
G → - T

Arcade says it must be true that - G → T
----
Only if G is selected would T not be selected. Therefore, if G then no T (G → - T)

How can it be true that if no G is selected that T has to be selected?

You correctly switched the order to "Only if G is selected would T not be selected." However, you're wrong in translating that as "Therefore, if G then no T (G → - T)."

Think about this similar statement: Only if my son sleeps through the night will I be refreshed in the morning.

Does that mean that him sleeping through the night definitely leads to me being refreshed? No. I could be awoken by something else. (Yes, this is me venting about my current lack of sleep!)

But, if I did wake refreshed, it must be true that he slept through the night.

The "only if" almost always indicates the necessary part of the condition.

That clear it up?