Question

Explain why each of the correspondences pictured below is not a one-to-one mapping from set $A$ to set $B$.

Short answer

None of the picture is one-to-one mapping.

Step-by-step solution

Step 1. Given Information.

The given sets are,

Step 2. Explanation.

A mapping from set A to set B is called a one-to-one mapping if every member of set B has exactly one pre image in set A.

In picture a, two elements in set B have single pre image in set A.

In picture b, one element is vacant; it means no pre image in set A.

In picture c, there are in single element in set B has two pre image in set A.

In picture d, in set A, there is no any image in set B.

Step 3. Conclusion.

Therefore, it is clear that it in all four cases this function is not one-to-one function.