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Chapter 2: Q15 (page 42)

Consider the following statements:

Reflexive Property: Robot A is as rusty as itself.

Symmetric Property: If Robot A is as rusty as Robot B, then Robot B is as rusty as Robot A.

Transitive Property: If Robot A is as rusty as Robot B and Robot B is as rusty as Robot C, then Robot A is as rusty as Robot C.

A relation such as 鈥渋s as rusty as鈥� that is reflexive, symmetric, and transitive is an equivalence relation. Which of the following are equivalence relations?

a. Is rustier than

b. Has the same length as

c. Is opposite (for rays)

d. Is coplanar with (for lines)

Short Answer

Expert verified

鈥楬as the same length as鈥� is an equivalence relation.

Step by step solution

01

Step 1. Reflexive property.

The reflexive property states that, if p is any number then p=p.

02

Step 2. Symmetric property.

Symmetric property states that, if p=qthen q=p.

03

Step 3. Transitive property.

Transitive property states that, if p=qand q=rthen p=r.

04

Step 4. Description of step.

A relation such as 鈥淚s as rusty as鈥� that is reflexive, symmetric and transitive is an equivalence relation then 鈥渉as the same length as鈥� among the given options is an equivalence relation.

Therefore option 鈥�b鈥�, that is, 鈥榟as the same length as鈥� is a correct option.

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Most popular questions from this chapter

State the number that is paired with the bisector of 鈭�CDE.

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m鈭�3+m鈭�4=180

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