CHAPTER 1 : RELATIONS

Let R be the relation in the set N given by R = {(a,b); a = b – 2 , b > 6} Is the relation reflexive?

• YES

• NO

The smallest equivalence relation R on set A = {1,2,3} is

• {(1,1) ,(2,2),(3,3)}

• {(1,1) ,(2,2),(3,3),(1,2),(2,1)}

• {(1,1) ,(2,2),(3,3), (2,1)}

• none of these

Given set A = {a,b,c}. An identity relation in set A is

• R= {(a,b),(a,c)}

• R = {(a,a),(b,b), (c,c) }

• R= {(a,a),(b,b), (c,c), (a,c)}

• R= {(c,a),(b,a), (a,a)}

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

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

Let A={a,b,c}. Which of the following relations on A are reflexive?

• {(a,a),(c,c),(a,b)}

• {(a,a),(a,b),(b,c),(b,b),(c,c)}

• {(b,b),(c,c),(c,b)}

• none of these

Relation R in the set A of all the books in a library of a college,given by R = {(x, y) : x and y have same number of pages} is

• Reflexive

• Symmetric

• Transitive

• All of above