Which one of the following statements most accurately characterizes a difference between the two passages?

Nishant on May 5, 2020

Could be True, Not necessarily false, Could be false, not necessarily true

I'm a little confused as to whether could be true and could be false mean the same thing or not? I know that could be true equals not necessarily false, but doesn't could be true mean the same thing as could be false?

Replies

Ben on May 5, 2020

Hi Nishant-Varma, thanks for reaching out!

The question you are asking right now is one that confuses a lot of people even until test day and it is good that you are sorting it out early.

Could be true and could be false are different due to the following:

When a question asks you about a variable being in a certain slot for example (e.g. M in slot 3).

If it is asking you if it could be true then it is asking you whether there is any possibility whatsoever that it could be true. If it is possible that M can go into slot 3, then it is could be true.

If it is asking you if it could be false, then it is asking you whether there is any possibility whatsoever that it could be false (some other slot). If it is possible that M can go into any other slot, then it could be false that M is third.

This sounds pretty similar. However, where they really diverge is the endpoints.

Could be true goes from Must be true to could be true. But it does not include Cannot Be True. Otherwise it would not be could be true.

Could be false goes from Must be false to could be false. But it does not include Must be true. Otherwise it would not be could be false.

I hope this helps clear it up. But if you have any leftover questions, please let me know and I will elaborate further.

Nishant on May 6, 2020

So could be true CAN include must be true, but could be false does not include must be true?
And could be false CAN include cannot be true, but could be true does not include cannot be true?

Ben on May 7, 2020

Exactly. Does this help clear it up?

Nishant on May 7, 2020

Yes, thank you!