Question

If A = {a,b,c,d} mention the type of
relations on A given below, which of
them are equivalence relations ?
(i) {(a, a), (b, b)}​

Answer 1

Answer:

ANSWER

Step 1.

Consider the relation R1 = { (a,a) }

it is reflexive ,symmetric and transitive

similarly R2= {(b,b)} , R3= {(c,c)} are reflexive ,symmetric and transitive

Step 2.

Also R4 = {  (a,a) ,(b,b),(c,c), (a,b),(b,a)}

it is reflexive as(x,x)∈R(a,a)∈R for all x∈a,b,ca∈1,2,3

it is symmetric as (x,y)∈R=>(y,x)∈R(a,b)∈R=>(b,a)∈R for all  x,y∈a,b,ca∈1,2,3

also it is transitive as (a,b)∈R,(b,a)∈R=>(a,a)∈R(1,2)∈R,(2,1)∈R=>(1,1)∈R

Step. 3

The relation defined by R = {(a,a), (b,b) , (c,c) , (a,b), (a,c),(b,a),(b,c), (c,a),(c,b)}

is reflexive symmetric and transitive

 

Thus Maximum number of equivalance relation on set  

A={a,b,c}A={1,2,3} is 5

Explanation:

Answer 2

Explanation:

12th

Maths

Relations and Functions

Introduction to Relations

Total number of equivalence...

MATHS

Total number of equivalence relations defined in the set S={a,b,c} is ?

MEDIUM

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ANSWER

Step 1.

Consider the relation R1 = { (a,a) }

it is reflexive ,symmetric and transitive

similarly R2= {(b,b)} , R3= {(c,c)} are reflexive ,symmetric and transitive

Step 2.

Also R4 = {  (a,a) ,(b,b),(c,c), (a,b),(b,a)}

it is reflexive as(x,x)∈R(a,a)∈R for all x∈a,b,ca∈1,2,3

it is symmetric as (x,y)∈R=>(y,x)∈R(a,b)∈R=>(b,a)∈R for all  x,y∈a,b,ca∈1,2,3

also it is transitive as (a,b)∈R,(b,a)∈R=>(a,a)∈R(1,2)∈R,(2,1)∈R=>(1,1)∈R

Step. 3

 The relation defined by R = {(a,a), (b,b) , (c,c) , (a,b), (a,c),(b,a),(b,c), (c,a),(c,b)}

is reflexive symmetric and transitive

 

Thus Maximum number of equivalance relation on set 

A={a,b,c}A={1,2,3} i