Into Function
A function f: A → B is said to be into if there exists even a single element in B having no pre-image in A.
So, f is into range (f) ⊂ B.
Example:
Let A = {2, 3, 5, 7} and B = {0, 1, 3, 5, 7}
Let f: A → B: f(x) = (x – 2) then
f(2) = (2 – 2) = 0
f(3) = (3 – 2) = 1
f(5) = (5 – 2) = 3
f(7) = (7 – 2) = 5
Thus, every element in A has a unique image in B
Now ∃ 7 ∈ B having no pre-image in A
Hence, f is into.