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hello and welcome to the first lecture of conditional proof now conditional proof is another uh i will say tool which we use apart from rules of influence and rules of replacement and it is a very i will say powerful tool because it helps us solving a lot of questions which are usually uh difficult say if if you have taken the rules of inference if you have seen a lot of questions on rules of influence or if you have seen a lot of questions on rules of replacement as well so those questions can be made little more simpler using the conditional proof now how this conditional proof is applied ah i will discuss but before that let us try to understand that what is the theory like suppose if you like like i may take a question first that suppose if a question is given like this like suppose on line number one you are given a wedge b ah implies c dot b okay and then you are given another premise as b which e implies uh f and therefore the conclusion is a implies f so suppose if this question is given right so if this question is given to us how to apply conditional proof now first thing first conditional proof is applied on now there are certain conditions which needs to be fulfilled before you can apply conditional proof conditional proof will be applied only when you have a question which is having an implication as the main connective in the confusion so the conclusion must have the conclusion must have material implication as the main connective fine so this is the condition which needs to be fulfilled this is something which you should understand that unless you have in the question an implication in the conclusion you cannot apply conditional proof how to apply and all these things we will be discussing but before that try to understand that you need an implication first thing second thing suppose if there are more than one implication like suppose if the conclusion is a implies b implies c okay so you can apply conditional proof more than once so uh i will write it down i will explain it with the help of an example like suppose you need to apply conditional proof twice in a question so in fact i will write that conditional proof we call it cp the short form of conditional proof is cp so cp can be applied more than once in the question so this is another point which you need to know before we want to understand the theory of conditional proof so two things which you should remember first thing is that a conditional proof can be applied only when you have a material implication or implication as the main connective so this is the first thing that you need to remember the second thing is that you can apply like suppose if you have...