Determine if the following functions are homomorphisms / embeddings / isomorphisms. You must only answer: "not a homomorphism", "homomorphism buffnot an embedding", "embedding but not an isomorphism", "isomorphism".  If not specified, the interpretations of the symbols in the signatures are the standard ones.  a. n ↦ 2n from (ℕ, 0, +, ·) to (ℕ, 0, +, ·).  b. n ↦ 2n from (ℕ, 0, +) to A := (ℕ, 0A, +A), where 0A is 1 and +A is the usual multiplication.  c. (x, y) ↦ x - y from A := (ℝ2, 0A, +A) to (ℝ, 0, +), where 0A := (0, 0) and +A is the usual coordinate-wise addition of points in ℝ2.

d) Give an example of a function from A to B that isone-to-one. e) Give an example of a function from A to B that isonto. f) How many functions are there from B to A? Explainbriefly.

For the relations: A x B, such that: A = {37, 38, ..., 42} and B = {42, 43,..., 47} Count how many possible ways N₁ to have functions P: A B N₁ = Count how many possible ways N₂ to have as one-to- one function N₂ = Count how many possible ways N3 to have y NOT onto. N3 =

Click and drag the domain and range on the left to their corresponding functions defined on the right, provided lambda (A) is the empty string. The function that assigns to each pair of positive integers the first integer of the pair Domain: Zt and range: {0, 1} The function that assigns to each positive integer its largest decimal digit Domain: Z+ and range: Z+ P The function that assigns to a bit string the number of ones minus the number of zeros in the string Domain: set of bit strings, and range: {1, 11, 111, ...} Domain: ZxZ+ and range: Z+ X The function that assigns to each positive integer the largest integer not exceeding the square root of the integer X The function that assigns to a bit string the longest string of ones in the string Domain: set of bit strings, and range: {A, 1, 11, 111, ...} Domain: Zt and range: (0, 1) Domain: Zt and range: Z Domain: set of all bit strings, and range: Z Domain: set of bit strings, and range: [1, 11, 111, ...) Domain: ZxZ+ and range: Z+…