Let the universe of discourse of x and y be the set of integers. Given: (1) ThereExists x ThereExists y [ (x + y = 4) AND (x - y = 1) ]. (2) ThereExists x ThereExists y [x^2 + y^2 = 26]. Select one of the following choices: a. (1) is False and (2) is True. ○ b. (1) and (2) are True. c. (1) and (2) are False. d. (1) is True and (2) is False.
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![Let the universe of discourse of x and y be the set of integers.
Given:
(1) ThereExists x ThereExists y [ (x + y = 4) AND (x - y = 1) ].
(2) ThereExists x ThereExists y [x^2 + y^2 = 26].
Select one of the following choices:
a. (1) is False and (2) is True.
○ b. (1) and (2) are True.
c. (1) and (2) are False.
d. (1) is True and (2) is False.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd3be9fc5-49dc-4987-93dc-30b0d6519ab7%2F4ae4d2b6-685c-41ae-8a8f-dab7c60962c1%2Fxpgmjxf_processed.png&w=3840&q=75)
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- Given A = {1,2,3} and B={u,v}, determine. a. A X B b. B X BQl: The Collatz conjecture function is defined for a positive integer m as follows. (COO1) g(m) = 3m+1 if m is odd = m/2 if m is even =1 if m=1 The repeated application of the Collatz conjecture function, as follows: g(n), g(g(n)), g(g(g(n))), ... e.g. If m=17, the sequence is 1. g(17) = 52 2. g(52) = 26 3. g(26) = 13 4. g(13) = 40 5. g(40) = 20 6. g(20) = 10 7. g(10) = 5 8. g(5) = 16 9. g(16) = 8 10. g(8) = 4 11. g(4) = 2 12. g(2) = 1 Thus if m=17, apply the function 12 times in order to reach m=1. Use Recursive Function.Let L be a line in the xy plane. If L is a vertical line, its equation is x=afor some real number a. Suppose L is not a vertical line and its slope is m. Then the equation of L is y=mx + b, where b is the y-intercept. If L passes through the point (x0,y0), the equation of L can be written as y –y0=m(x –x0). If (x1,y1)and (x2,y2)are two points in the xy plane and x1≠x2, the slope of the line passing through these points is m = (y2-y1)/ (x2-x1). Write a program that prompts the user to enter two points in the xy plane. The program outputs the equation of theline and uses ifstatements to determine and output whether the line is vertical, horizontal, increasing, or decreasing. If L is a nonvertical line, output its equation in the form y=mx + b.
- For (∃ x)(P(x,b)) Would an example of this being true if the domain was all the Avengers and x was green skin, then "b" being the Hulk would make this true. Am example of this being false would be: If the domain was all integers and x was positive, even integers and "b" was integers greater than zero.Suppose that the equation ax b .mod n/ is solvable (that is, d j b, whered D gcd.a; n/) and that x0 is any solution to this equation. Then, this equation has exactly d distinct solutions, modulo n, given by xi D x0 C i.n=d / fori D 0; 1; : : : ; d 1If A = {1, 2, 6} and B = {2, 3, 5}, then the union of A and B is
- If S = { x | 0 ≤ x ≤ 10}, A = { x | 1 ≤ x ≤ 5}, B = { x | 1 ≤ x ≤ 6}, and C = { x | 2 ≤ x ≤ 7}(a) S ⋃ C(b) A ⋃ B(d) A’ ⋂ C(c) A’⋃ (B ⋂ C)(e) (A ⋂ B) ⋃ (B ⋂ C) ⋃ (C ⋂ A)On the Island of Knights and Knaves we have two people A and B. A says: Exactly one of us is a knight if and only if B is a knight. B says: A is a knight if I’m a knight. determine if A and B are each a knight or a knave. (The problem might have no solutions, one solution, or many solutions.)If A = {0, 1), B = {1, 2, 3), then (AUB) x B is equal to:
- 1. A set of integers are relatively prime to each other if there is no integer greater than 1 that divides all the elements. Furthermore, in Number Theory, it is known that the Euler function,ϕ (n), expresses the number of positive integers less than n that are relatively prime with n. Choose the alternative that has the correct value of ϕ(n) for every n below. A) ϕ(5) = 4 B) ϕ(6) = 2 C) ϕ(10) = 3 D) ϕ(14) = 6 E) ϕ(17) = 16Dingyu is playing a game defined on an n X n board. Each cell (i, j) of the board (1 2, he may only go to (2, n).) The reward he earns for a move from cell C to cell D is |value of cell C – value of cell D|. The game ends when he reaches (n, n). The total reward - is the sum of the rewards for each move he makes. For example, if n = 1 2 and A = 3 the answer is 4 since he can visit (1, 1) → (1, 2) → (2, 2), and no other solution will get a higher reward. A. Write a recurrence relation to express the maximum possible reward Dingyu can achieve in traveling from cell (1, 1) to cell (n, n). Be sure to include any necessary base cases. B. State the asymptotic (big-O) running time, as a function of n, of a bottom-up dynamic programming algorithm based on your answer from the previous part. Briefly justify your answer. (You do not need to write down the algorithm itself.)Let A {c, e,j, l, s, u, y, z}, which of the following is true? There may be more than one correct answer. OA. Ø C A B. {q,f, v, d} C A C. AC {I, y, s, u} D. {I, y, s, u} = {u, s, 1, y} E. {1, y, s, u} C A F. {u, s, 1, y} C {I, y, s, u}- OG. {e, s, l, g} CA