Logic axiome function

i dont even know where to start, im working on a little project of mine

lets say i have a string of axiom called alpha, and i need a function that would return in bool what the result is, no matter how big the axiom is

lets say we have a logic axiome presented as:

a | b | c | d

its not important what form it belongs, if you ask me, the logical axiom could look like this:
(a & b)|(c & d)

the end result should have a boolean output of ether true or false
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Can you give a more detailed explanation? I'm not sure how you're supposed to evaluate the example expressions you're giving without any values for a, b, etc. Is that meant to be a parameter?
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