Discrete Chapter 8 & 10

• reflexive

• symmetric

• transitive

• an equivalence relation

If A = {1, 2, 3}, B = {1, 4, 6, 9} and R is a relation from A to B defined by 'x is greater than y'. The range of R is

• {1, 4, 6, 9}

• {4, 6, 9}

• {1}

• none of these

Let R be a relation on N defined by x + 2y = 8. The domain of R is

• {2, 4, 8}

• {2, 4, 6, 8}

• {2, 4, 6}

• {1, 2, 3, 4}

Let A = {1, 2, 3} and R = {(1, 2), (2, 3), (1, 3)} be a relation on A. Then, R is

• neither reflexive nor transitive

• neither symmetric nor transitive

• transitive

• none of these

If R is the largest equivalence relation on a set A and S is any relation on A, then

• R = S

• none of these

If R is a relation on the set A = {1, 2, 3, 4, 5, 6, 7, 8, 9} given by x R y y = 3x, then R =

• {(3, 1), (6, 2), (8, 2), (9, 3)}

• {(3, 1), (6, 2), (9, 3)}

• {(3, 1), (2, 6), (3, 9)}

• none of these

Let R be a relation defined on {1,2,3} defined by R ={(1,2) ,(2,1)}. To make it transitive relation which ordered pair should be added ?

• (1,1)

• (2,3)

• (1,3)

• (2,2)

Let A ={3,5,7} and B ={2,6,10}. A relation R from A to B is defined as R ={(x,y) : x and y are relatively prime}. Then R^-1 =

• { (3,2),(3,10), (5,2),(5,6),(7,2),(7,6),(7,10)}

• { (2,3),(10,3), (2,5),(6,5),(2,7),(6,7),(10,7)}

• { (3,2),(3,10), (5,2),(6,5),(2,7),(6,7),(10,7)}

• { (2,3),(10,3), (2,5),(5,2),(5,6)}

A partial ordered relation is transitive, reflexive and

Let N = {1, 2, 3, ..... } be ordered by divisibility. Which of the following subsets is totally ordered?

• (2, 6, 24)

• (3, 5, 15)

• (2, 9, 16)

• (4, 15, 30)