Minimum Independence Assumptions needed for statement to be true?

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I am a bit confused on conditional independence:

Given the following independence assumptions: ⫫, ⫫, ⫫, ⫫|, ⫫|,⫫|

What is the minimal set of independence assumptions needed in order for the equation to be true?

(a) (,) = (|)()

If we know that (,) = (|Y)(), then it must be the case that (|)=(|Y). I am confused as to how knowing conditional probabilities will help with this?

(b) (|) = (|)() Again with this one I know that ()(|) = (,)P(x). Is there any information about X and Y being independent?

Thanks!