1 votes 1 votes Find a compound proposition logically equivalent to $p \rightarrow q$ using only the logical operator $\downarrow$? Mathematical Logic kenneth-rosen set-theory&algebra propositional-logic mathematical-logic descriptive + – siva140191 asked Jun 5, 2018 edited Mar 4, 2019 by Pooja Khatri siva140191 275 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
Best answer 2 votes 2 votes 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) $ Deepak Poonia answered Jun 5, 2018 selected Jun 5, 2018 by srestha Deepak Poonia comment Share Follow See all 0 reply Please log in or register to add a comment.