please add details and steps please dont skip the steps i want to learn this thing

Problem 9. Suppose T U{A} is a satisfiable set of formulae and T U{A} U {B} Ftaut 1. Is it necessarily the case that I taut B? Prove or give a countererample. Hint. It is in fact the case that I taut B. So you should prove that I Ftaut B is incorrect. You can proceed by either giving a countererample or proof by contradiction. The latter means assume I Flaut B and reach to a contradiction with the other two assumptions. Problem 9. Suppose T U{A} is a satisfiable set of formulae and T U{A} U {B} Ftaut 1. Is it necessarily the case that I taut B? Prove or give a countererample. Hint. It is in fact the case that I taut B. So you should prove that I Ftaut B is incorrect. You can proceed by either giving a countererample or proof by contradiction. The latter means assume I Flaut B and reach to a contradiction with the other two assumptions