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Unformatted text preview: is in X . • if ϕ and ψ are in X , then ∨ ϕψ is in X . • if ϕ and ψ are in X , then → ϕψ is in X . • if ϕ and ψ are in X , then ↔ ϕψ is in X . 1 PROP* can be understood to contain the propositional formulas of PROP written in a diﬀerent notation. In this notation the connectives come in front of arguments, instead of in between them. For example, one writes ∧ p 1 p 2 instead of p 1 ∧ p 2 . Notice that with this notation no parentheses are used. (a) (2 points) Convert ∧ → p 1 ¬ p 4 ∨ p 7 p 9 to a regular propositional formula in PROP . (b) (2 points) Convert (( p 1 ∨ p 4 ) → (( ¬ p 7 ) ∨ p 9 )) to a formula in PROP* . (c) (6 points) Deﬁne a function recursively that maps the propositional formulas of PROP* to PROP . (d) (6 points) Deﬁne a function recursively that maps the propositional formulas of PROP to PROP* . 2...
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