Which is not a tautology formula


Which of the following formula is not tautology?

  1. (p →(pvq))
  2. ((p→~p)→~p)
  3. ((~q p) q)
  4. p v ~p


option 3 is the answer ,As option 1,2 and 4 are tautology formula.


as we know tautology is the condition where the output is true.
if we look for the options 1,2 and 4 the output will be true (you can make a table of p and q with 2^2 combinations of 0 and 1 and can get the output, which is true) for option 3 we have ~pq which is nothing. either we have p and q, p or q, ~p,~q.
we have nothing like pq.


1, 2 and 4 all are Tautologies. i.e. the truth table of these options always contain True as output.
3rd option is typing error.