Hi, an agnostic here ... just agnostic.

[TheHuxleyAgnostic]

For any claim: X, you can believe X is true, believe X is false, or have no belief either way. 

Person A: belief X is true, no belief X is false
Person B: no belief X is true, no belief X is false
Person C: no belief X is true, belief X is false

I'm missing the context here, but if one believes X to be true, then by extension, they must believe X is not false.

Yes, that's what "true" means ... "not false". 

A: belief P, no belief ~P
B: no belief P, no belief ~P
C: no belief P, belief ~P