optimization – Converting 4 variable if else condition to Linear integer program

There are four variables: x1, x2, x3, x4.

If you choose either x3 or x4 or both – then you should chose exactly one of x1 or x2.
If you choose neither x3 or x4 – then there is no restriction in ch0osing x1 or x2.

I have come up with the following if else logic for this, but cannot proceed from there.

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Can you let me know how to come up with a integer linear program with this understanding?