8. Prove the claim using induction: In any prefix of a (well-formed) proposi- tional formula, the number of left parentheses is greater than or equal to the number of right parentheses. State clearly what is the declarative sentence P(F) that you are proving. an s any string of the form al (A prefix of a string ai 0 S m Sn.) a,n where 9. Prove the claim using induction: Every prefix of a propositional for mula F . is an empty string, or has more left than right parentheses, or equals F State clearly what is the declarative sentence P(F) that you are proving. 8. Prove the claim using induction: In any prefix of a (well-formed) proposi- tional formula, the number of left parentheses is greater than or equal to the number of right parentheses. State clearly what is the declarative sentence P(F) that you are proving. an s any string of the form al (A prefix of a string ai 0 S m Sn.) a,n where 9. Prove the claim using induction: Every prefix of a propositional for mula F . is an empty string, or has more left than right parentheses, or equals F State clearly what is the declarative sentence P(F) that you are proving