Select the property(ies) of the given function f:Z→Zf(x)=9x+1 O fis a bijection f is one-to-one None of the proposed answers fis a function f is onto
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- subject: discrete structures there may be several correct answers Find a minimal expansion as a Boolean sum of Boolean products of the function?|(?̅?) + (? ↓ ?)?̅+ ??̅̅̅.Computer Science In function f(x) ->y the domain of x is continuous in the range 1-10how many equivalence classes are there in this case?Given a functor parameterised type m and comes with a function return :: a -> m a, show how functions with the following types can each be defined in term of the other: (>>=) :: m a -> (a -> m b) -> m b combine :: m (m a) -> m a
- Expand on the concept of Black Box and then go into detail on primivitive functions:Discrete mathematics applied to computer science: homework question. Let f : A → A be a function in the domain A =/= ∅. Confirm or deny, with justification: f is a bijection if and only if the composition f ◦ f is a bijection. I don't understand how I should approach this problem. Thank you for your gracious help.For the first problem, in parts b and c, how are the variables being taken from functions that they are not defined in? To clarify, in part c, how is the variable "b" taken from fun2 when it is not defined in that in function. Shouldn't the answer there just be "b(fun1)"
- Determine if each function is injective, surjective or bijective. Give one counterexample for each that it is not. 1. function f from {a,b,c,d} to itself, where f(a) = d, f(b) = b, f(c) = a, f(d) = cA function from Boolean algebra B to Boolean algebra B∗ is a homomorphism if it satisfies the definition of isomorphism, but is not necessarily a bijection. f(x+y)=f(x)&f(y) • f(x·y)=f(x)∗f(y) • f(x′) = (f(x))′′ (a) Prove f(0) = 0∗ (b) Give an example of a homomorphism from P({1,2,3}) to P({1,2}). (It will not be an isomorphism—why?)Suppose f : A → B is an injective function. Show that there is a function g : B → A such thatg ◦ f = idA. Here, idA : A → A is the identity function on A, i.e., the function that satisfies idA(a) = afor all a ∈ A. (Assume f is non-trivial, i.e., A ̸= ∅!)
- Take the polymorphic type for example: (c, h) -> (c -> h) -> (h, h) Make a list of all conceivable total functions of this type as lambda expressions, omitting any that behave similarly to the ones you've already put down.Complete the axiomatization by using and add a rule of universal generalization (∀1∀1) ∀x A→A(y/x) ∀x A→A(y/x),provided yy is free for xx in AA (∀2∀2) ∀x(A→B) → (A→∀x B) ∀x(A→B) → (A→∀x B),provided xx does not occur free in Alooking for atom code for the following Trace the function f as demonstrated in class for the function call f("No", 2): void f(string s, int len) { if(len == 0) { return; } f(s, len-1); cout << s[len-1];} int main() { f("No", 2"); return 0;}