the conclusion is true Therefore the argument is valid This form of valid argument is called the law of detachment because the

Question

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

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