Associativity of Connectives :
Here brackets are very important in order to tell us where to perform calculations in arithmetic and logic. By using these brackets we evaluate the truth of sentences in logic. By assuming , we want to add 10, 5 and 7. So now we could do this: (10 + 5) + 7 = 22. Otherwise we could do this: 10 + (5 + 7) = 22. So in such case, we can alter the bracketing and then the answer still comes out the same. It good complement to say that addition is associative it means that it has this property with respect to bracketing.
The ^ and ? connectives are as associative. Because this makes sense, and the order in that we check truth values doesn't matter where we are working with sentences only involving ? or ^only involving . For case in point expect that we wanted to know the truth of P ^ (Q ^ R). Rather than any other action, we just find to check that every proposition is true, such case the whole sentence will be true, or else the whole sentence will be false. There is no matter how the brackets are arranged, and hence the ^ is associative.