RELATIONS

If A={a,b,c} theen R={(b,c)}, then R is

• Reflexive only

• Symmetric only

• Transitive only

• equivalence relation

Let A={1,2,3}, and R is {(1,1),(1,2),(1,3), (2,2), (2,3), (3,3)}, then R is

• reflexive but not symmetric

• reflexive but not transitive

• symmetric and transitive

• neither symmetric nor transitive

For real numbers x and y define xRy iff x-y+√2 is an irrational number. then R is

• reflexive

• symmetric

• transitive

• none of these

Tags

CCSS.HSN.RN.B.3

the maximum number of equivalence relation in set A={1,2,3} is

• 1

• 2

• 4

• 5

Tags

CCSS.HSS.CP.B.9

Let N be a set of natural numbers and relation R on N be defined as

R = { (a,b):a,b are natural numbers and a + b =10 }

R is

• reflexive

• symmetric

• transative

• none of these

Set A = { x: x is a whole number less than 13 } . R is a relation on A given by R = { (a,b ) : |a - b| is multiple of 4 }. Equivalence class of 2 is

• { 1, 2, 4 , 6 }

• { 0 , 4, 8 }

• {2, 6, 10 }

• 2, 6 , 10

A = { 2, 4, 6, 8 } . R is a relation on A such that

R = { (a,b): a is greater than b }. Equivalence class of 8 is

• 2,4,6

• {2, 4, 6 }

• { 2, 4, 6, 8 }

• Does not exists

Let set A = { 1, 2, 3, 4 } and R is a relation on A such that

R = { (1, 1), (2,2), (3,3) , (4,4) } then

• R is not reflexive relation

• R is not symmetric relation

• R is not transitive relation

• R is an equivalence relation

R is a relation on set of natural numbers such that

R = { (a,b) : a + 4b = 10}

• R is a reflexive relation.

• R is a symmetric relation.

• R is a transitive relation.

• All of the above.

R is a relation on set N of natural numbers Defined by

R = { (a,b) : b = a + 1 , a , b < 7 }.

• R is a reflexive relation.

• R is a symmetric relation.

• R is a transitive relation

• None of the above