Given A = {1, 2, 3, 4} B = {2, 5, 10, 17}, a E A and b E B

The mapping rule for f maps 1 to 2, 2 to 5, 3 to 10 and 4 to 17.

(A) Write the mapping rule in the format of the listing method. Display the mapping using the listing format.
(B) Write the mapping rule in the format of function notation. Show the mapping using a function notation.
(C) Identify, using the most appropriate language, the type of mapping from A to B.

(A) The mapping rule in the format of the listing method is as follows:

1 -> 2
2 -> 5
3 -> 10
4 -> 17

This mapping rule can be represented using the listing format, where the elements on the left (1, 2, 3, 4) are mapped to the corresponding elements on the right (2, 5, 10, 17).

(B) The mapping rule in the format of function notation is:

f: A -> B
f(1) = 2
f(2) = 5
f(3) = 10
f(4) = 17

In function notation, the mapping rule is represented by stating that function 'f' maps elements from set A to set B. Then, each element in set A is assigned its corresponding image in set B.

(C) The type of mapping from A to B can be identified as a function. A function is a special type of mapping where each element from the domain (A) is mapped to a unique element in the co-domain (B). In this case, each element in set A is mapped to a unique element in set B as per the given mapping rule.

(A) The mapping rule in the format of the listing method is as follows:

f: A → B
1 → 2
2 → 5
3 → 10
4 → 17

The mapping using the listing format:

{(1, 2), (2, 5), (3, 10), (4, 17)}

(B) The mapping rule in the format of function notation is as follows:

f(x) = y

f(1) = 2
f(2) = 5
f(3) = 10
f(4) = 17

The mapping using function notation:

f: A → B
f(x) = y

(C) The type of mapping from A to B is a one-to-one (injective) mapping.