The set S is defined recursively as follows: (1) (0,0) E S, (1,1) E S. (3)...

 

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The set S is defined recursively as follows: (1) (0,0) E S, (1,1) E S. (3) (2) If (n-1, x) E S and (n − 2,y) ES then (n,x + y) ES. Membership for S can always be demonstrated by (finitely many) successive applications of clauses above. (minimality clause) (a) Is (2,2) ES? Explain. (b) Is (10,55) E S? Explain (c) What is S? (base clause) (recursion clause) [1 mark] [1 mark] [2 marks] The set S is defined recursively as follows: (1) (0,0) E S, (1,1) E S. (3) (2) If (n-1, x) E S and (n − 2,y) ES then (n,x + y) ES. Membership for S can always be demonstrated by (finitely many) successive applications of clauses above. (minimality clause) (a) Is (2,2) ES? Explain. (b) Is (10,55) E S? Explain (c) What is S? (base clause) (recursion clause) [1 mark] [1 mark] [2 marks]

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a Yes 22 E S This is because 11 E S and 00 E S Using the recursion clause we can see that 2 x y E S ... View the full answer