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.