1.Suppose that C is generated from a set B= {a,b} by the binary operation f and the unit operation g . List all the elements of C, . How many elements can they have C, y C,? Remember that C, is the set of all points x such that some construction sequence of length n ends with x, and so B= C cC, c C; ... 2. Prove that (A →^4.) it is not a formula

Q: 3.(1) List all the partitions of the set S = {1, 2, 3, 4}. (2) From (1), determine how many…

A: First five partitions are given in step one and the rest is given in step 2  1. 1, 2, 3, 4 2. 1, 2,…

Q: The permutations p = (3 5 4), q= (1 5 2 3) and r = (1 5 2) are elements of S5. pal, m. (a) Find each…

A: (a) To find each of the given permutations in cycle form, we will apply the permutations…

Q: Show that D^2 = {(x, y) ∈ E^2: x^2+y^2 ≤ 1} ⊂ E^2 and the space containing a single point are…

A: In algebraic topology, two topological spaces are said to be homotopy equivalent if there exists a…

Q: A. Compute the total number of sets (of size 5) containing exactly 2 elements from X and 3 elements…

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Q: Let f= (14723 5 6) and g = (1 5 3 264) be permutations in S. What is the second line of fin two-line…

A: Introduction: Permutation businesses are mathematical businesses whose individuals are permutations…

Q: 6. Let s, be the number of different symmetric trains of length n which are built out of cars which…

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Q: Let X = {a, b, c}. For each of the following binary relations on X, check the boxes next to the…

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Q: Give a recursive definition with initial conditions of the set S SEE IMAGE

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Q: Consider the Datalog programs P1 (left) and P2 (right) below, which use relations R(A, B) and S(A,…

A: Option (B) is correct because T3 and T4 include same set of tuples

Q: A scientist noticed that the population of a certain country could be represented by the following…

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Q: Determine the number of strings of length 10 from the alphabet {A, B, C} that contain exactly 3 A's…

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Q: d) Determine whether Prove it, if not give Ris e) Determine whether If not Ris antisymmetric a…

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Q: . You are traveling on a grid from (2, 2) to (18, 18). The only steps you can make are either to…

A: Solution of the question is given below.

Q: At the imaginary university e/UT there are 101 students in their first year at M&CS. In their first…

A: Given: Double counting Total students=101 To find: k

Q: Theorem 2. Let R and S be binary relations on a set X. Then, (a) (R-1)-1 = R. (b) (RUS)-1 = R-'Us-!.…

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Q: . Let S = P({1,2,3,4,5}.. Define equivalence class of the set {1,2,3}. equivalence relation ~ by X~Y…

A: Consider the given information: