# Assignment D

This exercise tests students their understanding of the concept ‘Rule of Inference‘.

Common Mistakes:

• Often students try to use these rules to replace a part of a wff by another wff. For instance, one would say, if $\mathcal{H}\vdash A\vee B\vee C$, then $\mathcal{H}\vdash B\vee A\vee C$. However, the rules do not justify this.
• Several students incorrectly took the rules as axioms, and use Transitive Law to deduce $\vdash A\vee .B\vee C\supset A\vee B\vee C$. However, in this exercise, you are asked to prove that from $A\vee .B\vee C$ one may infer $A\vee B\vee C$, or equivalently, if $\vdash A\vee .B\vee C$ then $\vdash\vee A\vee B\vee C$. It is important to distinguish between our meta-language and the language of our logistic system.