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Homework Statement
Use the logical equivalences [tex] p \rightarrow q \equiv \sim p \vee q [/tex] and [tex] p \leftrightarrow q \equiv (p \rightarrow q) \wedge (q \rightarrow p) [/tex] to rewrite the statement form:
[tex](p \rightarrow (q \rightarrow r)) \leftrightarrow ((p \wedge q) \rightarrow r) [/tex]
Homework Equations
None
The Attempt at a Solution
My initial assumption is to set this up as:
Let P == [tex](p \rightarrow (q \rightarrow r))[/tex]
Let Q == [tex]((p \wedge q) \rightarrow r) [/tex]
Then plug in from there with the equivalences to get:
[tex] (p \rightarrow q) \wedge (q \rightarrow p) [/tex]
Furthermore:
[tex] (\sim p \vee q) \wedge (q \rightarrow p) [/tex]
Is this the right approach, or am I starting it out wrong?
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