Consider a set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. What will be the computer representation for set containing the numbers which are multiple of 3 not exceeding 6? Describe injective, Surjective and bijective function with example.

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Given, Set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Here, we know the set containing the numbers which are multiple of 3 not exceeding is {3, 6}

And its computer representation is its corresponding bit string i.e.

0 0 1 0 0 1 0 0 0 0

Let A and B be two non-empty sets. A function f from A to B is set of ordered pairs with the property that for each element x ∈ A there is a unique element y ∈ B.

Injective Function:

A function \(f : A \to B\) is said to be is said to be injective (or one-to-one, or 1-1) if for any x, y ∈ A, f(x) = f(y) impiles x = y.

All this means is that for a function to be one-to-one every distinct element in A has a distinct image in B.

- Hamro CSIT

 

 

Surjective  Function:

If every element b in B has a corresponding element a in A such that f(a) = b. It is not required that a is unique; The function f may map one or more elements of A to the same element of B.

 

Bijective Function:

Surjective Example

A fnction f from A to B is said to be bijective if it is both injective and surjective.

Bijective Function Example

If function is bijective, its inverse exists.

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