====== Logic Problems ======

===== Q.1 =====
(a) Verify that the propositional formula
  (P IMPLIES Q) OR (Q IMPLIES P)
is valid.

(b) The valid formula of part (a) leads to sound proof method: to prove that an implication is true, just prove that its converse is false. For example, from elementary calculus we know that the assertion
  If a function is continuous, then it is differentiable
is false. This allows us to reach at the correct conclusion that its converse,
  If a function is differentiable, then it is continuous
is true, as indeed it is.

But wait a minute! The implication
  If a function is differentiable, then it is not continuous
is completely false. So we could conclude that its converse
  If a function is not continuous, then it is differentiable,
should be true, but in fact the converse is also completely false. So something has gone wrong here. Explain what.

QMARK