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I am wondering if some symbols such as the ones in propositional logic have precedence over others in drawing parse trees.

For example, the sentence: p ∧ q → r, would take precedence over in becoming the root of the parse tree or vice versa?
Or is there no precedence meaning, or could be used the root?

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Operator precendences have to be specified, either in the grammar or using other means. There is no inherent precendence to rules, but you can fix one arbitrarily.

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