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###### Exerciz 2 Let n be pasitive integer The Koal of this exercise is to give combinatorial proof for the identityFn+ =2() where Fn is the n-th Fibonacci number starting with Fi = Fz = 1 Recall that, COM binatorial proof;, one uSually counts the same quantity in two different ways: suhset 5 â‚¬ {1, n} is said to be slithy if all elements of 5 are geatu than the cardinality of 5_ For example the empty sct is slithy (), but {1} is not slithy:Let Sn denote the number of slithy subsets of {1= (i) Establi

Exerciz 2 Let n be pasitive integer The Koal of this exercise is to give combinatorial proof for the identity Fn+ = 2() where Fn is the n-th Fibonacci number starting with Fi = Fz = 1 Recall that, COM binatorial proof;, one uSually counts the same quantity in two different ways: suhset 5 â‚¬ {1, n} is said to be slithy if all elements of 5 are geatu than the cardinality of 5_ For example the empty sct is slithy (), but {1} is not slithy:Let Sn denote the number of slithy subsets of {1= (i) Establish the recurrence relation sn+1 Sn-1: Deduce thuat Sn (quals the left-hand side By counting the slithy subsets of size k = 0.1, show that sn equals the right-hand side

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