Question

Let A={1,2,3,...,100}and R be the relation defined as"is cube of" on A. Find the domain and range of R

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Answer 1

R={ (1,1),(2,8),(3,27),(4,64)}

Domain = {1,2,3,4}

Range= {1,8,27,64}

Step-by-step explanation:

Relation: A relation is an ordered of pair.

There are three types of relation

• Reflexive
• Symmetric
• Transitive

Reflexive: A relation said to be reflexive on a set A, if (a,a)∈R for every a∈ A

Symmetric: A relation said to be symmetric on set A, if (a,b)∈ R for every a,b∈ A ⇒ (b,a)∈R

Transitive: A relation said to be transitive on a set A , (a,b),(b,c)∈R for every a,b and c ∈ A ⇒(a,c)∈R.

Here A ={1,2,3,........,100} and R be the relation defined as "is cube of" on A.

    Domain                                        Range

       1                                                     1

       2                                                    8

       3                                                   27

       4                                                   64

R={ (1,1),(2,8),(3,27),(4,64)}

Domain = {1,2,3,4}

Range= {1,8,27,64}