Match the following in List - I and List - II, for a function f:
Match the following in List - I and List - II, for a function f:
|
|
List – I |
|
List - II |
|
(a) |
∀ x ∀ y (f (x) = f(y) → |x = y) |
(i) |
Constant |
|
(b) |
∀ y ∃ x (f (x) = y) |
(ii) |
Injective |
|
(c) |
∀ x f (x) = k |
(iii) |
Surjective |
A. (a) – (i), (b) – (ii), (c) – (iii)
B. (a) – (iii), (b) – (ii), (c) – (i)
C. (a) – (ii), (b) – (i), (c) – (iii)
D. (a) – (ii), (b) – (iii), (c) – (i)
Please scroll down to see the correct answer and solution guide.
Right Answer is: D
SOLUTION
A function is a way of matching the members of a set A to set B.
Explanation:
Injective function:
A function f: A -> B is injective if each b belongs to B has at most one preimage in A that is there is at most one a belongs to A such that f(a) = b. An injective function is also known as one to one function.
∀ x ∀ y (f (x) = f(y) → |x = y), here it represents an injective function.
Surjective function:
A function f: A -> B is surjective if each b belongs to B has at least one preimage that is there is at least one a belongs to A such that f(a) = b. A surjective function is also known as onto function.
∀ y ∃ x (f (x) = y), it represents a surjective function.
Constant function:
A constant function is a function whose value remains the same for every input value.
Here, ∀ x f (x) = k, it represents a constant function.