Write a computer algorithm, in pseudocode, to test whether a relation R defined on a finite set A is symmetric, for A = {a[1],a[2],...,a[n]}.

Consider F = {BC -> D, B -> E, CE -> D, E -> CA, BF -> G} and R(A,B,C,D,E,F,G) 1.Find a minimal cover for F. 2.Find all many keys for R.

Show that the language of strings over {1} of the form 1^n where n is a Fibonacci number is not regular.

Question 5 Refer to the following graph and choose the option that reflects the row for node 3 of the D(2) matrix generated by the Floyd-Warshall Algorithm. If you are solving this programmatically, be careful about zero-based indices in most languages. The graph below has 1-based indexing. 1 O 32042-8 3 O-42 327620 -5 Infinity O 87 Infinity 9 0 Infinity O 0204-1-8 10 5 -8

Suppose you were given two sequences, S1 and S2 of n elements, possibly containing duplicates, on which a total order relation is defined. Describe an efficient algorithm for determining if S1 and S2 contain the same set of elements. Analyze the running time of this method. 

The format P(X) represents as a power set of given "X", (of all X's subsets)   Now, assume there are two sets  A= {q, w, e, r} and B = {w, r, f}. (a) What are the elements of P(A) ∩P(B )?(b) What is the cardinality of P(A ∪B )?(c) What is |P(A) ∪P(B )|?