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Define the many-one function. Give an example.

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Many-one Function

A function f: A→ B is said to be many-one if two or more than two elements in A have the same image in B.

Example:

Let A = {-1, 1, 2, 3} and B = {1, 4, 9}

Let f: A → B: f(x) = x2 Ɐ x ∈ A

Then, each element in A has a unique image under f in B

f is a function from A to B such that

f(-1) = (-1)2 = 1

f(1) = 12 = 1

f(2) = 22 = 4

f(3) = 32 = 9

Here, two elements namely -1 and 1 have same image 1 ∈ B.

Hence, f is many-one.

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