Let f:N2 Z+ be defined as f (x, y) -2"3'. Which of the following best describes f? (Note: A2 is another way of writing A x A) total and onto and not one-to-one total and not one-to-one and not onto total and one-to-one and not onto one-to-one and not onto and not total onto and not one-to-one and not total one-to-one and onto and not total not one-to-one and not onto and not total total, one-to-one, and onto

Every element of domain(N²) has a unique image in co-domain but for every y∈Z⁺ there does not exit pair (p,q)∈N². Thus, the function f one to one and total but not onto function.

So, Correct option is option(C).

Onto Functions: A function in which every element of Co-Domain Set has one pre-image.

One-to-One Functions: A function in which one element of Domain Set is connected to one element of Co-Domain Set.

Total function: A function which is defined for all inputs of the right type, that is, for all of a domain.

Let f : N² --> Z⁺ be defined as

f(x,y) = 2ˣ3ʸ

then, f is not onto because for z∈ Z⁺

there is (x,y)∈N²

f(x,y) = z is not possible.

f is one to one because for (x₁, y₁) , (x₂,y₂)∈N²

such that f(x₁,y₁) = f(x₂,y₂)

=> 2ˣ¹3zʸ¹= 2ˣ²3ʸ²

=> x₁ = x₂ and y₁ = y₂

=>( x₁ ,y₁) = (x₂, y₂)

so, f is one to one. Every element of domain(N²) has an image in Co-domain(Z⁺). Thus, f is total function.

Hence, f is one to one and total but not onto.

To learn more about One-One and Onto function, refer:

https://brainly.com/question/11237515

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