# Identities, Free Algebras

Given a type F and a set of variables X and p; q P TpXq show that TpXq |ù p q iff p q (thus TpXq does not satisfy any interesting identities).

EDITED VERSION:

Exercise 11.1 from Burris-Sankapanavar: A Course in Universal Algebra:

Given a type $\mathcal F$ and a set of variables $X$ and $p, q \in T(X)$ show that $\mathbf T(X)\models p\approx q$ iff $p=q$. (Thus $\mathbf T(X)$ does not satisfy any interesting identities).

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 Still a formatting issue – Rustyn Yazdanpour Dec 23 '12 at 7:28 @mirabbasi Please accept, or at least comment on, answers to your previous questions, like this one, if you want people to take the time to help you with additional questions. You should show that you are at least reading and understanding the answers to your questions. – William DeMeo Dec 25 '12 at 21:59