the conclusion is true Therefore the argument is valid This form of valid argument is called the law of detachment because the conclusion q is detached from a premise namely p q It is also called the law of direct inference ii Law of contraposition or modus tollens To understand this law consider the following argument If Kali can draw then she will get a job Kali will riot get a job Therefore Kali can t draw Taking p arid q as in i above you can see that the premises arc p q and q The conclusion is p So the argument is P q 9 P If you check you ll find that this is a valid form of argument There are two more rules of inference that most commonly form tlie basis of several proofs The following exercise is about them 3 E4 You will find three arguments below Convert each of them into the language of symbols and check if they are valid i Either the eraser is white or oxygen is a metal The eraser is black Therefore oxygen is a metal i c pq Aq p ii If Madhu is a sarpanch she will head the panchayat If Madhu heads the panchayat she will decide on property disputes Therefore if Madhu is a sarpanch she will decide on property disputes iii Either Munna will cook or Mumi will practise Karate If Munni practises Karate then Munna studies 1 Munna does not study Therefore Munni will practise Karate E5 Write down one example each of modus ponens and modus tollens As you must have discovered the arguments in E4 i and ii arc valid The first one is an example of a disjunctive syllogism The second one is an example of a hypothetical syllogism Thus a disjunctive syllogism is of the form pvq P i e pv q Ap q q And a hypothetical syllogism is of the form 2 P q qr i e p q qr pr Method Modus tollen method of de