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2. (24 pts) True/False. Circle T or F. No explanation needed. (a) T F If Ris...
2. Let S 11,2,3,4,5, 6, 7,8,91 and let T 12,4,6,8. Let R be the relation on P (S) detined by for ...
2. Let S 11,2,3,4,5, 6, 7,8,91 and let T 12,4,6,8. Let R be the relation on P (S) detined by for all X, Y E P (s), (X, Y) E R if and only if IX-T] = IY-T]. (a) Prove that R is an equivalence relation. (b) How many equivalence classes are there? Explain. (c) How mauy elements of [ø], the equivalence class of ø, are there? Explain (d) How many elements of [f1,2,3, 4)], the equivalence class of (1,2,3,...
1. Let A= {0,1}2 U... U{0,1}5 and let < be the order on A defined by...
1. Let A= {0,1}2 U... U{0,1}5 and let < be the order on A defined by (s, t) E< if and only if s is a prefix of t. (We consider a word to be a prefix of itself.) (a) Find all minimal elements in A. (Recall that an element x is minimal if there does not exist y E A with y < x.) (b) Are 010 and 01101 comparable? 2. Give an example of a total order on...
(2 pts each) Find a different equivalent form of the statements. Justify your answers using Laws...
(2 pts each) Find a different equivalent form of the statements. Justify your answers using Laws of equivalence or otherwise. (a) Not all men are Scientists. (b) If you are a computer science major you will need discrete mathematics. (10 pts) Let R be an equivalence relation on a non empty set X. So R C X X X. R is reflexive: Vx E X, (x,x) E R, R is symmetric: Vx, y E X, (x,y) E R = (y,x)...
17-26 true or false questions 17. The smallest positive real number is c, where c = card(0,1). 18. To show that two sets A and B are equal, show that x A and x B. 19. If (vx)P(e) is false, then P...
17-26
true or false questions
17. The smallest positive real number is c, where c = card(0,1). 18. To show that two sets A and B are equal, show that x A and x B. 19. If (vx)P(e) is false, then P(x) is never true for that domain. 20. If R is a relation on A and if (a, a) is true for some a in A, then R is reflexive. 21. If f:A → B is a function, then...
I. Let each of R, S, and T be binary relations on N2 as defined here: R-[<m, n EN nis the smallest prime number greater than or equal to m] S -[< m, n> EN* nis the greatest prime number less...
I. Let each of R, S, and T be binary relations on N2 as defined here: R-[<m, n EN nis the smallest prime number greater than or equal to m] S -[< m, n> EN* nis the greatest prime number less than or equal to m] (a) Which (if any) of these binary relations is a (unary) function? (b) Which (if any) of these binary relations is an injection? (c) Which (if any) of these binary relations is a surjection?...
Please Do it clearly and ASAP UNIC HaHdheld ull, 130 points is a "perfect" score. Good luck! Part I. True False. Circle T if the statement is always true, and F if the statement is at leas...
Please Do it clearly and ASAP
UNIC HaHdheld ull, 130 points is a "perfect" score. Good luck! Part I. True False. Circle T if the statement is always true, and F if the statement is at least sometimes false. [10 pts] 1) T F RREF(A) is unique. 2) T F The solution set to "Ax b" is a vector space. 3) T F Every square matrix is diagonalizable. 4) T F Adding a column to a column of annxn A...
this is true and false for C++ (1 point each) Circle T for true or F...
this is true and false for C++
(1 point each) Circle T for true or F for false for the following questions. 1. T/F The Boolean expression b1 || b2 evaluates to true if either Boolean value (b1, b2) is true. T/F The code we write in C++ (e.g. code in file project1.cpp) is referred to as source code. 2. 3. T/F The statement float scores[3][3] creates 3 arrays, each containing 3 floating-point variables. T/F For loops work best when...
Please answer this question and it’s subparts 3. (25 points) Part I11: Functions a. (7 pts)...
Please answer this question and it’s subparts
3. (25 points) Part I11: Functions a. (7 pts) Consider functions f and g with the same domain X and co-domain Y, eg, f : X → Y and gX -Y. Must it be true that fng is a function? Why or why not? glx) b. (4 pts) Draw an arrow diagram for a function that is injective but not surjective. ほ, v/ c. (15 pts) Let S be the set of all...
For each of the following statements, circle T (True) or F (False) Serial execution of a...
For each of the following statements, circle T (True) or F (False) Serial execution of a set of transactions is guaranteed to preserve database consistency. When using the two-phase locking protocol, two transactions can hold shared locks on the same data element at the same time. The recovery manager ensures the Atomicity property of a transaction by committing all operations of aborted transactions. A B+ tree index, that starts a root node, is rarely used in a relational database. Deadlocks...
23 43 Problem 6. (5 pts each) True or False (Circle one and state your seaon) If t) is a solution of the DE: "+(t-t)y+Ay- 5, then so is the f Reason: rue Fa b. Let f and g be two functions, such...
23 43 Problem 6. (5 pts each) True or False (Circle one and state your seaon) If t) is a solution of the DE: "+(t-t)y+Ay- 5, then so is the f Reason: rue Fa b. Let f and g be two functions, such that F(s)L0) and Go)-Li defined on (0, oo). If f(t) S 9(t) for allt 2 0, then F(o) S Glo) for als True F Reason: c. There exists a piecewise continuous and ex that LIf(0)]-3 exponential order...
2. Let S 11,2,3,4,5, 6, 7,8,91 and let T 12,4,6,8. Let R be the relation on P (S) detined by for all X, Y E P (s), (X, Y) E R if and only if IX-T] = IY-T]. (a) Prove that R is an equivalence relation. (b) How many equivalence classes are there? Explain. (c) How mauy elements of [ø], the equivalence class of ø, are there? Explain (d) How many elements of [f1,2,3, 4)], the equivalence class of (1,2,3,...
1. Let A= {0,1}2 U... U{0,1}5 and let < be the order on A defined by (s, t) E< if and only if s is a prefix of t. (We consider a word to be a prefix of itself.) (a) Find all minimal elements in A. (Recall that an element x is minimal if there does not exist y E A with y < x.) (b) Are 010 and 01101 comparable? 2. Give an example of a total order on...
(2 pts each) Find a different equivalent form of the statements. Justify your answers using Laws of equivalence or otherwise. (a) Not all men are Scientists. (b) If you are a computer science major you will need discrete mathematics. (10 pts) Let R be an equivalence relation on a non empty set X. So R C X X X. R is reflexive: Vx E X, (x,x) E R, R is symmetric: Vx, y E X, (x,y) E R = (y,x)...
17-26
true or false questions
17. The smallest positive real number is c, where c = card(0,1). 18. To show that two sets A and B are equal, show that x A and x B. 19. If (vx)P(e) is false, then P(x) is never true for that domain. 20. If R is a relation on A and if (a, a) is true for some a in A, then R is reflexive. 21. If f:A → B is a function, then...
I. Let each of R, S, and T be binary relations on N2 as defined here: R-[<m, n EN nis the smallest prime number greater than or equal to m] S -[< m, n> EN* nis the greatest prime number less than or equal to m] (a) Which (if any) of these binary relations is a (unary) function? (b) Which (if any) of these binary relations is an injection? (c) Which (if any) of these binary relations is a surjection?...
Please Do it clearly and ASAP
UNIC HaHdheld ull, 130 points is a "perfect" score. Good luck! Part I. True False. Circle T if the statement is always true, and F if the statement is at least sometimes false. [10 pts] 1) T F RREF(A) is unique. 2) T F The solution set to "Ax b" is a vector space. 3) T F Every square matrix is diagonalizable. 4) T F Adding a column to a column of annxn A...
this is true and false for C++
(1 point each) Circle T for true or F for false for the following questions. 1. T/F The Boolean expression b1 || b2 evaluates to true if either Boolean value (b1, b2) is true. T/F The code we write in C++ (e.g. code in file project1.cpp) is referred to as source code. 2. 3. T/F The statement float scores[3][3] creates 3 arrays, each containing 3 floating-point variables. T/F For loops work best when...
Please answer this question and it’s subparts
3. (25 points) Part I11: Functions a. (7 pts) Consider functions f and g with the same domain X and co-domain Y, eg, f : X → Y and gX -Y. Must it be true that fng is a function? Why or why not? glx) b. (4 pts) Draw an arrow diagram for a function that is injective but not surjective. ほ, v/ c. (15 pts) Let S be the set of all...
For each of the following statements, circle T (True) or F (False) Serial execution of a set of transactions is guaranteed to preserve database consistency. When using the two-phase locking protocol, two transactions can hold shared locks on the same data element at the same time. The recovery manager ensures the Atomicity property of a transaction by committing all operations of aborted transactions. A B+ tree index, that starts a root node, is rarely used in a relational database. Deadlocks...
23 43 Problem 6. (5 pts each) True or False (Circle one and state your seaon) If t) is a solution of the DE: "+(t-t)y+Ay- 5, then so is the f Reason: rue Fa b. Let f and g be two functions, such that F(s)L0) and Go)-Li defined on (0, oo). If f(t) S 9(t) for allt 2 0, then F(o) S Glo) for als True F Reason: c. There exists a piecewise continuous and ex that LIf(0)]-3 exponential order...
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