$1$ The $(30$ points$)$ Consider the following rules: AB AC BD CD CB E a$)$ Draw the inference chain. b$)$ Given that E and Bare facts, carry out forward chaining. What is fact? c$)$ Given Eis fact, carry out backward chaining with B as the goal. Is a solution possible? d$)$ Following c$),$ would the state of D be known during inference? Explain.