(iii) Proof by cases or by exhaustion
This method of proving a statement p ⇒ q is possible only when p can be split into
several cases, r, s, t  (say) so that  p = r ∨  s ∨  t (where “∨ ” is the symbol for “OR”) If the conditionals
r ⇒ q;
s ⇒ q;
and
t ⇒ q
are proved, then (r ∨  s ∨  t) ⇒ q, is proved and so p ⇒ q is proved The method consists of examining every possible case of the hypothesis It is
practically convenient only when the number of possible cases are few