Recall that a combinatorial proof for an identity proceeds as follows: 1. State a counting question....

 

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Recall that a combinatorial proof for an identity proceeds as follows: 1. State a counting question. 2. Answer the question in two ways: (i) one answer must correspond to the left-hand side (LHS) of the identity (ii) the other answer must correspond to the right-hand side (RHS). 3. Conclude that the LHS is equal to the RHS. With that in mind, give a combinatorial proof of the following identity: () = ()+ (,") +n², where n 2 2. Recall that a combinatorial proof for an identity proceeds as follows: 1. State a counting question. 2. Answer the question in two ways: (i) one answer must correspond to the left-hand side (LHS) of the identity (ii) the other answer must correspond to the right-hand side (RHS). 3. Conclude that the LHS is equal to the RHS. With that in mind, give a combinatorial proof of the following identity: () = ()+ (,") +n², where n 2 2.

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Proof The expression on the lefthand side is the number of 2subsets of a 2nset Let P be a 2nset and ... View the full answer