Past exam of the logic and set theory course of the University of Oxford / 2008 / A / 1 / c / c

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- Solution c

Solution

A logical formula. Both

p_{1}

and

p_{2}

are propositional variables, so

(p_{1} \to p_{2})

and

(p_{2} \to p_{1})

are logical formulas. Applying the binary logical implication formation rule to this ordered pair of logical formulas gives the displayed whole expression. This supplies a construction of its formula syntax tree rather than merely checking that its parentheses balance.

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