Describe each of the following sets by listing its elements: a. {x | x ∈ N and x2 − 5x + 6 = 0} b. {x | x ∈ R and x2 = 19} c. {x | x ∈ N and x2 − 2x − 8 = 0}} d. {x | x ∈ Z and x ∗ x = 4}
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Describe each of the following sets by listing its elements:
a. {x | x ∈ N and x2 − 5x + 6 = 0}
b. {x | x ∈ R and x2 = 19}
c. {x | x ∈ N and x2 − 2x − 8 = 0}}
d. {x | x ∈ Z and x ∗ x = 4}
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- Given the following sets: U= {1,2,3,4,5,6,7,8,}, A={1,4,5,7}, B= {2,5,6,7,}, and C= {3,4,6,7} Complete the following set operations: a. A U(BUC) b. (A N (B N C))' . c. (A N B) U ( A N C) d. (A N B')U (A N C')Please help me in this question: 15/ Direct mapping is set associative mapping with a set size of _____ . a. 1 b. 2 c. N / 2 d. N Thank you!Implement the following Racket functions: Reflexive? Input: a list of pairs, L and a list S. Interpreting L as a binary relation over the set S, Reflexive? returns #t if L is a reflexive relation over the set S and #f otherwise. Examples: (display "Reflexive?\n") (Reflexive? '((a a) (b b) (c c)) '(a b c)) ---> #t (Reflexive? '((a a) (b b)) '(a b c)) ---> #f (Reflexive? '((a a) (a s) (b b) (c c)) '(a b c)) ---> #f (Reflexive? '() '()) ---> #t You must use recursion, and not iteration. You may not use side-effects (e.g. set!).
- What are disjoint sets?a. Disjoint sets are sets having common elements.b. Disjoint sets are sets having no common elements.c. Disjoint sets are sets that have only one elements.d. Disjoint sets are sets containing all the elements being considered.In the following problems ((f) - (j)) you are given the description of a set. Your task is to write down the set in the formal language of set theory by specifying the membership condition of the set. There are many possible answers here, but make sure that the condition you specify actually determines which elements belong to that set. (h) Assume the numbers in this set are natural numbers N. {0, 10, 20, 30, 40, 50, . . . } (i) Ecin U (j) The intersection of Ecin U and F.d. A grouping of a set's elements into non-empty subsets in such a way that every element is included in one and only one of the subsets is known as __________.
- Define function p:cat represents set concatenation ◦, which concatenates every pair of strings from both sets using racket. We can specify set concatenation as p1 ◦ p2 = {u · v | u ∈ p1 ∧ v ∈ p2}. Alternatively, we give an inductive specification: ∅ ◦ p2 = ∅ p1 ◦ p2 = prefix(u, p2) ∪ (p'1◦ p2) if p1={u} ∪ p'1.Let A = {2,3,4,5,8}, B = {2,3,4,7}, C = {0,1,4,6,7,8} List the elements of the following sets. If there is more than one element write them separated in commas. A∩B=A∪B=(B∪C)∩A=B∪(C∩A)=If A = {}, Discuss briefly using significant words why set A is an empty set…
- Implement the following Racket functions: You must use recursion, and not iteration. You may not use side-effects (e.g. set!). Transitive? Input: a list of pairs, L. Interpreting L as a binary relation, Transitive? returns #t if L is a transitive relation and #f otherwise. Examples: (display "Transitive? \n") (Transitive? '((a b) (b c) (a c))) ---> #t (Transitive? '((a a) (b b) (c c))) ---> #t (Transitive? '((a b) (b a))) ---> #f (Transitive? '((a b) (b a) (a a))) ---> #f (Transitive? '((a b) (b a) (a a) (b b))) ---> #t (Transitive? '())---> #tDefine X union Y. How is the union of X and Y denoted? Define X intersect Y. How is the intersection of X and Y denoted Define X and Y are disjoint sets. Define the difference of sets X and Y. How is the difference denoted What is a universal set? What is the complement of the set X? How is it denoted? Define symmetric difference of X and Y. How is the symmetric difference denoted? Draw a Venn diagram for all set operations above.This is last __________ the set of all elements in the collection; one of the fundamental operations through which sets can be combined and related to each other