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Define a new logical connective ⋆ as follows: P ⋆ Q is true if P is...

Define a new logical connective ⋆ as follows: P ⋆ Q is true if P is false or Q is false. (That is, P ⋆ Q is only false if P and Q are both true.)

Show that the operator ∼ (“not”) and the connectives ∨ (“or”), ∧ (“and”), and =⇒ (“if... then...”) can all be written in terms of ⋆ only. To get you started, ∼ P always has exactly the same truth value as (that is, is logically equivalent to) P ⋆ P : make sure you show why!

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