Implement the following Racket functions: Symmetric-Closure Input: a list of pairs, L. Interpreting L as a binary relation, Symmetric-Closure should return the symmetric closure of L. Examples: (Symmetric-Closure '((a a) (a b) (b a) (b c) (c b))) ---> '((a a) (a b) (b a) (b c) (c b)) (Symmetric-Closure '((a a) (a b) (a c))) ---> '((a a) (a b) (a c) (b a) (c a)) (Symmetric-Closure '((a a) (b b))) ---> '((a a) (b b)) (Symmetric-Closure '()) ---> '()

3,

give a recurrence relation that describes the sequence, answer both boxes.

The following two relations R and S have one attribute storing integers. Assume that a join is performed on this attribute. R = { 4, 3, 1, 6, 2, 9, 0, 5, 8, 7 } S = { 3, 4, 5, 8, 0, 2, 1, 6, 7, 9} Show the order of tuples output for the following join algorithms: (for example Sort Join would give (0,0), (1,1),...,(9,9) ) 1.One pass join where M=12 and R is put in memory: 2.Merge-sort-join with M=5: 3.Hash Join with three buckets and M=4. Assume R is the build relation and S is the probe relation. Also assume bucket 0 is output first. Output: