Im currently new to understanding the propositional logic and I am really confused on the difference between p ↔ q and p ≡ q.
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1See List of logic symbols: usually, none. – Mauro ALLEGRANZA Nov 20 '17 at 13:14
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Usually they mean the same thing, and each book will use one or the other, not both. But if your book uses both, you'll need to find out what that particular book means by it. There might be a “glossary of symbols” at the front or the back that may help. – MJD Nov 20 '17 at 13:15
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In some contexts, $\leftrightarrow$ is used for the propositional conncetive bi-conditional while $\equiv$ is used for logical equivalence (both usually read: iff). – Mauro ALLEGRANZA Nov 20 '17 at 13:15
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2See the similar post: what's-the-difference-between-biconditional-iff-and-logical-equivalence – Mauro ALLEGRANZA Nov 20 '17 at 13:37