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Kenneth Rosen Edition 6th Exercise 1.5 Question 51 (Page No. 63)
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Find a compound proposition logically equivalent to $p \rightarrow q$ using only the logical operator $\downarrow$?
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We know : $P \rightarrow Q $ $\equiv $ $P'+ Q \equiv \overline{P \overline{Q}} $
And $P ↓ Q \equiv \overline{P} \,\,\overline{Q}$
So, $\overline{P} ↓ Q \equiv P \overline{Q}$
$P \rightarrow Q $ $\equiv$ $((P↓P) ↓ Q ) ↓ ((P↓P) ↓ Q) $
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