Final answer:
The set {(4,2),(5,4),(3,7),(7,2)} is not a one-to-one mapping, as the codomain element '2' is mapped to by two different domain elements '4' and '7', thus violating the rule of a one-to-one mapping. The answer to whether the set is a one-to-one mapping is No.
Step-by-step explanation:
The question asks if the set {(4,2),(5,4),(3,7),(7,2)} represents a one-to-one mapping. A one-to-one mapping, also known as an injective function, is a type of function in which every element of the domain (the first component of the ordered pairs, in this context) is mapped to a unique element of the codomain (the second component of the ordered pairs). In other words, no element of the domain maps to the same element of the codomain more than once, and no element of the codomain is mapped to by more than one element of the domain.
In the provided set, let's consider each pair (a, b) as 'a' being from the domain and 'b' being from the codomain. We need to check whether each 'a' maps to a unique 'b' and vice versa. Upon inspecting the set, we observe that the domain elements (4, 5, 3, 7) are all unique, and the codomain elements (2, 4, 7, 2) feature a repetition: the number 2 appears twice as the output for two different input values (4 and 7).
Since the element '2' in the codomain is mapped to by both '4' and '7' from the domain, this violates the rule of one-to-one mapping. Therefore, the answer to whether the set is a one-to-one mapping is No.