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Chapter 14: Q1. (page 574)

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

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Given Information.

The given sets are,

02

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.

03

Step 3. Conclusion.

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

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Most popular questions from this chapter

Copy each figure on graph paper. Then draw the image by reflection in line k.
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  2. Is M a transformation?
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  4. Decide whether M maps the midpoint of PQ炉 to the midpoint of P'Q'炉.

A line with equation y=x+5 is reflected in the x-axis. Find an equation of the image line.

Mapping M maps points A and B to the same image point. Explain why the mapping M does not preserve distance.

In each exercise Rk:A鈫�A'. Find an equation of line k.
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