Types of relation

Consider the set A = {1, 2, 3} and the relation

R = {(1, 2), (1, 3)}.

• Reflexive

• Symmetric

• Transitive

• none of these

Let A = {1, 2, 3} and consider the relation

R = {1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1,3)}.Then R is

• reflexive but not symmetric

• reflexive but not transitive

• symmetric and transitive

• neither symmetric, nor

  transitive

Let R be a relation on the set N of natural numbers defined by nRm if n divides m. Then R is

• Reflexive and symmetric

• Transitive and symmetric

• Equivalence

• Reflexive, transitive but not

  symmetric

 For real numbers x and y, define xRy if and only if x – y is divisible by 3. Then the relation R is

• only reflexive

• Reflexive and symmetric

• Reflexive but not transitive

• Reflexive, symmetric and transitive

For the set A = {1, 2, 3}, define a relation R in the set A as follows:

R = {(1, 1), (2, 2), (3, 3), (1, 3)}.

Write the ordered pairs to be added to R to make it the smallest equivalence relation.

• (3,1),(1,2)

• (3,1)

• (3,2),(1,2)

• (3,2)

Let A = {0, 1, 2, 3} and define a relation R on A as follows:

R = {(0, 0), (0, 1), (0, 3), (1, 0), (1, 1), (2, 2), (3, 0), (3, 3)}.

Is R reflexive? symmetric? transitive?

Relation R in the set A = {1, 2, 3, ..., 13, 14} defined as

R = {(x, y) : 3x – y = 0}. Relation R is

• Reflexive

• Symmetric

• Transitive

• none of these

Relation R in the set N of natural numbers defined as

R = {(x, y) : y = x + 5 and x < 4}

• Reflexive

• Transitive

• Symmetric

• None of these

Relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)}

• Reflexive

• Symmetric

• Transitive

• none of these

Let R be the relation in the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4,4),(1, 3), (3, 3), (3, 2)}. Choose the correct answer.

• R is reflexive and symmetric but not transitive.

• R is reflexive and transitive but not symmetric.

• R is symmetric and transitive but not reflexive.

• R is an equivalence relation.