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 Example 4 Show that in any triangle ABC,
a = b cos C + c cos B
Solution Let p be the statement “ABC is any triangle” and q be the statement
“a = b cos C + c cos B”
Let ABC be a triangle