Oa.2
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A: I HAVE PROVIDED SOLUTION IN STEP2
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A: Lets see the solution.
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A: I have provided solution in step2
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A: I have provided a solution in step2
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- List all 3-tuples in the relation {(a,b,c)| abc = 6} where a, b and c are all positive integers.If P = { a,b,c,d,e } and Q = { a,q,r,s,e }, how many members has (P U Q) ?Let A={1,2,3} and B={4,5,6}. The set X={(1,4),(3,6),(2,4),(1,5)} is: O a relation between from A to B, but NOT a function from A to B O a set that has nothing to with A and B O equal to AxB O a function from A to B
- Given: Relation R = {(a,a), (a.b), (b,a). (b,b). (c,c)} and Set S = {a, b, c} Complete Relation R to be Transitive with Set SImplement the following Racket functions: Reflexive-Closure Input: a list of pairs, L and a list S. Interpreting L as a binary relation over the set S, Reflexive-Closure should return the reflexive closure of L. In mathematics, the reflexive closure of a binary relation R on a set X is the smallest reflexive relation on X that contains R. (https://en.wikipedia.org/wiki/Reflexive_closure) Examples: (Reflexive-Closure '((a a) (b b) (c c)) '(a b c)) ---> '((a a) (b b) (c c)) (Reflexive-Closure '((a a) (b b)) '(a b c)) ---> '((a a) (b b) (c c)) (Reflexive-Closure '((a a) (a b) (b b) (b c)) '(a b c)) ---> ((a a) (a b) (b b) (b c) (c c)) (Reflexive? '() '(a b c)) ---> '((a a) (b b) (c c)) You must use recursion, and not iteration. You may not use side-effects (e.g. set!).Let S be a set with |S| = 5. How many relations are there on S? A. 5! В. 55 C. 520 D. 525 Е. 225 A В E C.
- Implement the following Racket functions: Transitive-Closure Input: a list of pairs, L. Interpreting L as a binary relation, Transitive-Closure should return the transitive closure of L. Examples: (Transitive-Closure '((a b) (b c) (a c))) ---> '((a b) (b c) (a c)) (Transitive-Closure '((a a) (b b) (c c))) ---> '((a a) (b b) (c c)) (Transitive-Closure '((a b) (b a))) ---> '((a b) (b a) (a a) (b b))) (Transitive-Closure '((a b) (b a) (a a))) ---> '((a b) (b a) (a a) (b b)) (Transitive-Closure '((a b) (b a) (a a) (b b))) ---> '((a b) (b a) (a a) (b b)) (Transitive-Closure '()) ---> '() You must use recursion, and not iteration. You may not use side-effects (e.g. set!).Consider the following sets: A={2,4,5} B = {4,9,10,12} C = {1,3,8,9,10,12,14} I) Find all the elements of the set C\ (AUB): II) Find | C\ (AUB) | III)Let R is a relation on the set A = { 2, 4, 5}, with: R:A×A, write the resulted set R ?29. The complementary relation R is the set of ordered pairs {(a, b)|(a, b) € R}. Let R be the relation, R = {(a,b)|a divides b} on the set of positive integers. Thus, R equals to A. R = {(a, b)|a is the multiple of b} B. R = {(b, a)|b is the multiple of a} %3D C. R = {(b, a)|b divide a} D. R = {(a, b)|a does not divide b}
- 9. of 40 Let R(A, B, C, D, E) be a relation with the set of FD's: F%3 {D — С, С — D, D —— A, C — А, Е — С, Е — А, Е — В, В —C). Which of the following statements is NOT correct? Select one: O G = {D– C, C → D, D → A, E → B, B → C} is a canonical cover (minimal basis) of F. O H= {D– C, C → D, C → A, E –→ B, B → C} is a canonical cover of F. O F is a canonical cover of itself. O Both G and H are canonical covers of F.Given set A={1,2,3,4,5} and let R and S be a binary relation on set A. ? = {(?, ?) ? ??? | ?|? } ??? ? = {(2,1), (2,3), (3,4), (3,5), (4,5)} a.) Evaluate the Domain and Range of SoR. b.) Evaluate (???) −1 ??? ??? ̅̅̅̅̅.The domain for the relation R is the set of all integers. For any two integers, x and y, xRy if x evenly divides y. An integer x evenly divides y if there is another integer n such that y = xn. (Note that the domain is the set of all integers, not just positive integers.) Symmetric Transitive Anti-symmetric Reflexive